Neighbor Distance Research Articles

Distance Degree Sequence and Distance Neighborhood Degree Sequence of Vertices in Fuzzy Graphs and Some of Their Properties

Objectives: The objective of this study is to explore new types of sequences in fuzzy graphs namely distance degree sequence and distance neighborhood degree sequence of fuzzy graphs which may have various applications in the real world. Methods: In this paper, two unique sequences for each vertex of fuzzy graphs are given by means of its degree and neighborhood degree which are called as the distance degree sequence and distance neighborhood degree sequence of vertices of fuzzy graphs respectively. The n-tuple of the distance degree sequence of vertices of a fuzzy graph arranged in lexicographic order is called the distance degree sequence of the fuzzy graph and the n-tuple of distance neighborhood degree sequence of vertices of a fuzzy graph arranged in lexicographic order is called the distance neighborhood degree sequence of the fuzzy graph. Findings: The distance degree sequence and distance neighborhood degree sequence of fuzzy graphs are introduced. The properties of these sequences and the general forms of these sequences of various fuzzy graphs are given. The relationship between the distance degree sequence and distance neighborhood degree sequences is discussed. Novelty: The distance degree sequence of graphs has already been introduced. In fuzzy graph theory, the distance degree sequence and distance neighborhood degree sequence are introduced in this paper. Mathematics Subject Classification (202 0): 03E72, 05C72, 05C12. Keywords: Fuzzy graphs, Distance degree sequence, Distance neighborhood-degree sequence, Regular fuzzy graphs

Where Should Additional City Benches be Installed to Reduce Continuous Walking Distance? Comparison of Incrementally and Simultaneously Added Installations

ABSTRACTThe present locations of city benches show the required continuous walking distance, which can be defined as the distance from a city bench to the furthest neighboring one, called the furthest neighbor distance (FND). However, we lack a method for identifying where additional city benches should be installed incrementally to reduce the FND. The aim of this paper is thus (1) to develop a new method for determining the priority of the locations of new benches, subject to the number of city benches; and (2) to investigate the relationship between the priority and the reduction of the FND. The reduction of the FND is quantified based on the probability of an FND greater than 100 m. The empirical study around Tokyo Central Station showed that if reducing the probability of the FND being greater than 100 m is the top priority, additional city benches should be installed simultaneously.

High‐Frequency Electron Paramagnetic Resonance and Electron‐Nuclear Double Resonance Spectroscopy Study of the Ga Vacancy in β‐Ga2O3

The Ga vacancy (VGa) defect in β‐Ga2O3, generated by proton irradiation, is studied using high‐frequency electron paramagnetic resonance (EPR) and electron‐nuclear double resonance spectroscopy. The previous X‐band EPR studies of this defect, attributed to VGa2−, are extended to higher frequencies (240 GHz) and lower temperatures (T = 6 K). The spin Hamiltonian parameters of the VGa2− center are determined: electron spin S = 1/2, g‐tensor: gb = 2.0313, gc = 2.0079, and ga = 2.0025; the hyperfine interaction parameters with 2 equivalent Ga neighbors: Ab = 14.0 G, Ac = 14.6 G, and Aa* = 12.8 G for 69Ga; the superhyperfine interaction with distant Ga neighbors ASHF(69Ga) = 11 MHz; and the quadrupole interaction Qb(69Ga) = 0.32 MHz and Qb(71Ga) = 0.22 MHz. These results shall allow to refine the assignment of this center to a split vacancy or an unrelaxed VGa2− defect.

Two Automated Point Cloud Filtration Approaches using Principal Component Variance and Nearest Neighbor Distance

Two Automated Point Cloud Filtration Approaches using Principal Component Variance and Nearest Neighbor Distance

Dimensionality Reduction and Nearest Neighbors for Improving Out-of-Distribution Detection in Medical Image Segmentation

Clinically deployed deep learning-based segmentation models are known to fail on data outside of their training distributions. While clinicians review the segmentations, these models tend to perform well in most instances, which could exacerbate automation bias. Therefore, detecting out-of-distribution images at inference is critical to warn the clinicians that the model likely failed. This work applied the Mahalanobis distance (MD) post hoc to the bottleneck features of four Swin UNETR and nnU-net models that segmented the liver on T1-weighted magnetic resonance imaging and computed tomography. By reducing the dimensions of the bottleneck features with either principal component analysis or uniform manifold approximation and projection, images the models failed on were detected with high performance and minimal computational load. In addition, this work explored a non-parametric alternative to the MD, a k-th nearest neighbors distance (KNN). KNN drastically improved scalability and performance over MD when both were applied to raw and average-pooled bottleneck features. Our code is available at <a href='https://github.com/mckellwoodland/dimen_reduce_mahal'>https://github.com/mckellwoodland/dimen_reduce_mahal</a>

Quantitative Analysis about the Spatial Heterogeneity of Water Conservation Services Function Using a Space–Time Cube Constructed Based on Ecosystem and Soil Types

Precisely delineating the spatiotemporal heterogeneity of water conservation services function (WCF) holds paramount importance for watershed management. However, the existing assessment techniques exhibit common limitations, such as utilizing only multi-year average values for spatial changes and relying solely on the spatial average values for temporal changes. Moreover, traditional research does not encompass all WCF values at each time step and spatial grid, hindering quantitative analysis of spatial heterogeneity in WCF. This study addresses these limitations by utilizing an improved water balance model based on ecosystem type and soil type (ESM-WBM) and employing the EFAST and Sobol’ method for parameter sensitivity analysis. Furthermore, a space–time cube of WCF, constructed using remote-sensing data, is further explored by Emerging Hot Spot Analysis for the expression of WCF spatial heterogeneity. Additionally, this study investigates the impact of two core parameters: neighborhood distance and spatial relationship conceptualization type. The results reveal that (1) the ESM-WBM model demonstrates high sensitivity toward ecosystem types and soil data, facilitating the accurate assessment of the impacts of ecosystem and soil pattern alterations on WCF; (2) the EHSA categorizes WCF into 17 patterns, which in turn allows for adjustments to ecological compensation policies in related areas based on each pattern; and (3) neighborhood distance and the type of spatial relationships conceptualization significantly impacts the results of EHSA. In conclusion, this study offers references for analyzing the spatial heterogeneity of WCF, providing a theoretical foundation for regional water resource management and ecological restoration policies with tailored strategies.

Offspring may succeed well next to their relatives, but it needs particular traits.

There is ongoing debate about whether offspring perform best next to phylogenetically distantly related adult neighbours (due to the scarcity of enemies and competitors) or next to closely related adults (due to the abundance of mutualists). Here we hypothesise that relatedness of adult neighbours affects which traits confer performance rather than performance itself. We studied seed removal, seed germination and sapling growth in Sessile Oaks (Quercus petraea and hybrids), and how they depend on size, shape and other traits, under both closely and distantly related canopies, manipulating offspring-density, presence of insects, and fungi, and spatial proximity to oaks. We found that phylogenetic distance of adult neighbours affects only little performance of offspring but strongly which traits confer performance to offspring, in particular the size and shape of seeds and saplings. Differences in trait-performance relationships mostly disappear once insects or conspecific competitors are excluded (albeit exclusion of fungi reinforced these differences). Effects of phylogenetic distance of neighbours were not replaceable by the percentage of the gymnosperms among neighbours, nor the environmental conditions considered. We suggest that by responding to a biotic micro-mosaic of selection pressures, Sessile Oak flexibly succeeds in diverse neighbourhoods. Sessile Oak might maintain the potential for both, convergence with and divergence from phylogenetically distantly related species, thereby reinforcing or eroding phylogenetic signal of niches.

KAN-HyperMP: An Enhanced Fault Diagnosis Model for Rolling Bearings in Noisy Environments

Rolling bearings often produce non-stationary signals that are easily obscured by noise, particularly in high-noise environments, making fault detection a challenging task. To address this challenge, a novel fault diagnosis approach based on the Kolmogorov–Arnold Network-based Hypergraph Message Passing (KAN-HyperMP) model is proposed. The KAN-HyperMP model is composed of three key components: a neighbor feature aggregation block, a feature fusion block, and a KANLinear block. Firstly, the neighbor feature aggregation block leverages hypergraph theory to integrate information from more distant neighbors, aiding in the reduction of noise impact, even when nearby neighbors are severely affected. Subsequently, the feature fusion block combines the features of these higher-order neighbors with the target node’s own features, enabling the model to capture the complete structure of the hypergraph. Finally, the smoothness properties of B-spline functions within the Kolmogorov–Arnold Network (KAN) are employed to extract critical diagnostic features from noisy signals. The proposed model is trained and evaluated on the Southeast University (SEU) and Jiangnan University (JNU) Datasets, achieving accuracy rates of 99.70% and 99.10%, respectively, demonstrating its effectiveness in fault diagnosis under both noise-free and noisy conditions.

Nanoscale organization of cardiac calcium channels is dependent on thyroid hormone status.

Thyroid hormone dysfunction is frequently observed in patients with chronic illnesses including heart failure which increases risk of adverse events. This study examined effects of thyroid hormones (TH) on cardiac T-tubule (TT) integrity, Ca2+ sparks, and nanoscale organization of ion channels in excitation-contraction (EC)-coupling, including L-type calcium channel (Cav1.2), ryanodine receptor-type 2 (RyR2), and junctophilin-2 (Jph2). TH deficiency was established in adult female rats by propyl-thiouracil (PTU) ingestion for 8 weeks; followed by randomization to continued PTU without or with oral triiodo-L-thyronine (T3; 10 ug/kg/d) for two additional weeks (PTU+T3). Confocal microscopy of isolated cardiomyocytes (CM) showed significant misalignment of TTs, and increased Ca2+ sparks in thyroid-deficient CMs. Density-Based Spatial Clustering of Applications with Noise (DBSCAN) analysis of STochastic Optical Reconstruction Microscopy (STORM) images showed decreased (p<0.0001) RyR2 cluster number per cell area in PTU CMs compared to euthyroid (EU) control myocytes, and this was normalized by T3-treatment. Cav1.2 channels and Jph2 localized within 210 nm radius of the RyR2 clusters were significantly reduced in PTU myocytes, and these values were increased with T3 treatment. A significant percentage of the RyR2 clusters in the PTU myocytes had neither Cav1.2 or Jph2, suggesting fewer functional clusters in EC-coupling. Nearest neighbor distances between RyR2 clusters were greater (p<0.001) in PTU cells compared to EU and T3-treated CMs that corresponds to disarray of TTs at the sarcomere z-discs. These results support a regulatory role of T3 in the nanoscale organization of RyR2 clusters and co-localization of Cav1.2 and Jph2 in optimizing EC-coupling.

PerCNet: Periodic complete representation for crystal graphs

Crystal molecules are considered as graph structures in different representation methods. A reasonable crystal representation method should capture the local and global information. However, existing methods only consider the local information of crystal molecules by modeling the bond distance and bond angle of first-order neighbors of atoms, which leads to the issue that different crystals will have the same representation. To solve this many-to-one issue, we consider the global information by further considering dihedral angles. We propose a periodic complete representation of graph modeling and a calculation algorithm for infinite extended crystal materials. A theoretical proof for the representation that satisfies the periodic completeness is provided. Based on the proposed representation, we then propose a network for predicting crystal material properties, PerCNet, with a specially designed message-passing mechanism. To our best known, we are the first work that ensures the representation corresponds one-to-one with the crystal material based on graph modeling. Extensive experiments are conducted on two large-scale real-world material benchmark datasets. The PerCNet achieves the best performance among baseline methods in terms of MAE. Our code is available at https://github.com/JiaoHuang111/PerCNet.

Spatial pattern and landscape change prediction of blowouts in sandy grassland

Blowouts are a common type of wind-eroded landform found in sandy and desertified areas. They also represent a major degradative surface process affecting grassland ecosystems. Blowouts exacerbate changes in surface morphology through their effects on other surface phenomena including vegetation. In this paper, Xilingol League sandy grassland blowouts are taken as the research object, and the U.S. Keyhole satellite data and China’s Gaofen-1 satellite data are used as the data source, and the blowouts are extracted based on the 3 S technology for a total of six periods of high-resolution remote sensing image data in the study area from 1962 to 2023. The Landscape Pattern Index method and Fuzzy Land Use Simulation (FLUS) modelling applied to changes over the last six decades provided spatial evolution parameters for predicting future blowout distributions. Results showed that blowouts affecting the Xilingol grassland area increased by 16.81% over the past 60 years. The patch density (PD) increased by 0.9 per hectare. The mean proximity index (PROX_MN) and mean Euclidean nearest neighbour distance (ENN_MN) showed a tendency to decrease and then increase indicating initial expansion and then merging of adjacent blowouts to create the present landscape. The FLUS model used ten factors to predict changes in blowout distributions from 2023 to 2033. Factors included digital elevation model (DEM), slope, aspect, normalized difference vegetation index (NDVI), mean annual temperature, mean annual precipitation, population density, real GDP, distance to water, and distance to impervious surfaces. It was found that grassland area decreased by 6217.12 hm2 and blowout area decreased by 102.91 hm2. Results of this study can expand understanding of blowout morphodynamics in ecologically sensitive areas.

A new approach to K-nearest neighbors distance metrics on sovereign country credit rating

This study introduces feature importance K-nearest neighbors (FIKNN), an innovative adaptation of the K-nearest neighbors (KNN) algorithm tailored for classifying sovereign country credit ratings. The primary objective is to enhance KNN's predictive accuracy by integrating a feature importance mechanism derived from the random forest algorithm, which prioritizes significant features and reduces the impact of less relevant ones, refining the distance computation within KNN. Utilizing a comprehensive dataset of sovereign credit ratings, the performance of FIKNN was assessed against traditional KNN using various feature sets and bootstrap samples. The FIKNN model consistently outperformed the standard KNN by approximately 1% in classification accuracy, attributed to the weighted distance metric adjusting feature influence based on importance. Key findings indicate that FIKNN effectively manages datasets with varying feature relevance and demonstrates a positive correlation between feature diversity and model performance. Future research will explore other distance metrics and refine the feature importance weighting mechanism to broaden FIKNN's applicability in diverse predictive tasks.

Abstract A040: Multiplex fluorescent immunohistochemistry reveals immunosuppressive tumor microenvironment in COMPASS-like complex gene mutated pancreatic cancer

Abstract Background: Pancreatic ductal adenocarcinoma (PDAC) is highly resistant to chemoradiation and immune therapies. There is limited biomarker to identify subsets of PDAC that responds to immunotherapy or targeted therapy. We have identified a subset of PDACs (approximately 25%) carrying COMPASS-like complex (CLC) gene mutations. Analysis of the clinicopathologic and molecular features of this PDAC subset revealed that these tumors are an aggressive group of PDACs with poor or squamous histologic differentiation, increased rates of TP53 mutations, and poor patient survival compared to control PDACs. Our preliminary data showed that PDACs carrying mutations in two members of the CLC genes (KDM6A and KMT2D) have immunosuppressive tumor microenvironment (TME), suggesting that CLC genes are candidate biomarkers for immunotherapy. However, a comprehensive analysis of the immune composition, immune checkpoint expression, and the relationship between tumor cells and immune cells in CLC gene mutated PDACs compared to controls has not been performed. In this study, we characterized the immune composition in CLC gene mutated PDACs compared to paired control PDACs using tyramide signal amplification multiplex fluorescent immunohistochemistry (mfIHC). Methods: Human PDAC tissue slides were stained with 2 mfIHC panels and cell types were defined by different markers: panel 1 (PanCK, CD163, PD-L1, CD3, CD8, FoxP3) and panel 2 (PanCK, CD163, CD3, CD8, TIGIT, TIM3). Random image sections were selected in each sample (5∼8 sections per sample) and divided into wild-type (WT) group (n=57) and mutant group (n=41) and analyzed using InForm Cell Analysis software. Tissue segmentation training was performed to separate stromal and epithelial elements. Cell percentage, cell density, and nearest neighbor distance of each cell type were calculated using R program. Results: The CLC gene mutation is associated with elevated epithelial cells (ECs) and PDL1+ ECs and increased infiltration of exhausted cytotoxic T cells (TIGIT+/TIM3+ CD8 T cells). CLC gene mutated PDACs are characterized by spatial proximity between exhausted T cells (TIGIT+) and epithelial cells/antigen presenting cells (APCs). Higher number of epithelial cells is associated with reduced infiltration of helper T cells in the mutant PDAC tissue. We also observed that high numbers of APC in proximity to CD4 T cells were positively correlated with the proximity of EC and CD8 cytotoxic T cells as well as the proximity of CD4 T cells and cytotoxic T cells in the WT group but not in the CLC gene mutant group. Conclusion: Our results provide insight into the effects of CLC gene mutations on shaping the immune microenvironment of PDAC and suggest that CLC gene mutated PDACs have an immunosuppressive immune microenvironment than other PDACs and may respond differently to immunotherapy. Citation Format: Shungang Zhang, Elaina Daniels, Jake McGue, Hong Sun Kim, Dafydd Thomas, Timothy Frankel, Jiaqi Shi. Multiplex fluorescent immunohistochemistry reveals immunosuppressive tumor microenvironment in COMPASS-like complex gene mutated pancreatic cancer [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Advances in Pancreatic Cancer Research; 2024 Sep 15-18; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2024;84(17 Suppl_2):Abstract nr A040.

OS-PSO: A Modified Ratio of Exponentially Weighted Averages-Based Optical and SAR Image Registration.

Optical and synthetic aperture radar (SAR) images exhibit non-negligible intensity differences due to their unique imaging mechanisms, which makes it difficult for classical SIFT-based algorithms to obtain sufficiently correct correspondences when processing the registration of these two types of images. To tackle this problem, an accurate optical and SAR image registration algorithm based on the SIFT algorithm (OS-PSO) is proposed. First, a modified ratio of exponentially weighted averages (MROEWA) operator is introduced to resolve the sudden dark patches in SAR images, thus generating more consistent gradients between optical and SAR images. Next, we innovatively construct the Harris scale space to replace the traditional difference in the Gaussian (DoG) scale space, identify repeatable key-points by searching for local maxima, and perform localization refinement on the identified key-points to improve their accuracy. Immediately after that, the gradient location orientation histogram (GLOH) method is adopted to construct the feature descriptors. Finally, we propose an enhanced matching method. The transformed relation is obtained in the initial matching stage using the nearest neighbor distance ratio (NNDR) and fast sample consensus (FSC) methods. And the re-matching takes into account the location, scale, and main direction of key-points to increase the number of correctly corresponding points. The proposed OS-PSO algorithm has been implemented on the Gaofen and Sentinel series with excellent results. The superior performance of the designed registration system can also be applied in complex scenarios, including urban, suburban, river, farmland, and lake areas, with more efficiency and accuracy than the state-of-the-art methods based on the WHU-OPT-SAR dataset and the BISTU-OPT-SAR dataset.

DQ-NN and phantom routing for enhanced source location privacy for IoT under multiple source and destination

The Internet of Things (IoT) is now an essential component of our day-to-day lives. In any case, the association of various devices presents numerous security challenges in IoT. In some cases, ubiquitous data or traffic may be collected by certain smart devices which threatens the privacy of a source node location. To address this issue, a hybrid DL technique named Deep Q Learning Neural network (DQ-NN) is proposed for the Source Location Privacy (SLP) in IoT networks based on phantom routing. Here, an IoT network with multiple sources and destinations is considered first, and then the phantom node is chosen by analyzing neighbor list, energy, distance, and trust heterogeneity parameters. After that, multiple routes are created from the source node to the sink node via the phantom node. Finally, path selection is performed by the proposed DQ-NN. Moreover, DQ-NN is obtained by merging the Deep Q Learning Network (DQN) and Deep Neural Network (DNN). A simulation environment consisting of 150 nodes is created to study the effectiveness of performance and scalability. The proposed novel DQ-NN outperforms other existing algorithms, by recording a high network lifetime is 111.912, a safety period of 664970.7 m, an energy is 0.034 J, and a distance is 56.594 m.

Effects of the social environment on movement-integrated habitat selection

BackgroundMovement links the distribution of habitats with the social environment of animals using those habitats. Despite the links between movement, habitat selection, and socioecology, their integration remains a challenge due to lack of shared vocabulary across fields, methodological gaps, and the implicit (rather than explicit) historical development of theory in the fields of social and spatial ecology. Given these challenges can be addressed, opportunity for further study will provide insight about the links between social, spatial, and movement ecology. Here, our objective was to disentangle the roles of habitat selection and social association as drivers of movement in caribou (Rangifer tarandus).MethodsTo accomplish our objective, we modelled the relationship between collective movement and selection of foraging habitats using socially informed integrated step selection function (iSSF). Using iSSF, we modelled the effect of social processes, i.e., nearest neighbour distance and social preference, and movement behaviour on patterns of habitat selection.ResultsBy unifying social network analysis with iSSF, we identified movement-dependent social association, where individuals took shorter steps in lichen habitat and foraged in close proximity to more familiar individuals.ConclusionsOur study demonstrates that social preference is context-dependent based on habitat selection and foraging behaviour. We therefore surmise that habitat selection and social association are drivers of collective movement, such that movement is the glue between habitat selection and social association. Here, we put these concepts into practice to demonstrate that movement is the glue connecting individual habitat selection to the social environment.

Multi-dimensional Scaling from K-Nearest Neighbourhood Distances

Multi-dimensional Scaling from K-Nearest Neighbourhood Distances

Local means-based fuzzy k-nearest neighbor classifier with Minkowski distance and relevance-complementarity feature weighting

This paper introduces an enhanced fuzzy k-nearest neighbor (FKNN) approach called the feature-weighted Minkowski distance and local means-based fuzzy k-nearest neighbor (FWM-LMFKNN). This method improves classification accuracy by incorporating feature weights, Minkowski distance, and class representative local mean vectors. The feature weighting process is developed based on feature relevance and complementarity. We improve the distance calculations between instances by utilizing feature information-based weighting and Minkowski distance, resulting in a more precise set of nearest neighbors. Furthermore, the FWM-LMFKNN classifier considers the local structure of class subsets by using local mean vectors instead of individual neighbors, which improves its classification performance. Empirical results using twenty different real-world data sets demonstrate that the proposed method achieves statistically significantly higher classification performance than traditional KNN, FKNN, and six other related state-of-the-art methods.

A population code for spatial representation in the zebrafish telencephalon.

Spatial learning in teleost fish requires an intact telencephalon1, a brain region that contains putative analogues to components ofthe mammalian limbic system (for example, hippocampus)2-4. However, cells fundamental to spatial cognition in mammals-for example, place cells (PCs)5,6-have yet to be established in any fish species. In this study, using tracking microscopy to record brain-wide calcium activity in freely swimming larval zebrafish7, we compute the spatial information content8 of each neuron across the brain. Strikingly, in every recorded animal, cells with the highest spatial specificity were enriched in the zebrafish telencephalon. These PCs form a population code of space from which we can decode the animal's spatial location across time. By continuous recording of population-level activity, we found that the activity manifold of PCs refines and untangles over time. Through systematic manipulation of allothetic and idiothetic cues, we demonstrate that zebrafish PCs integrate multiple sources of information and can flexibly remap to form distinct spatial maps. Using analysis of neighbourhood distance between PCs across environments, we found evidence for a weakly preconfigured network in the telencephalon. The discovery of zebrafish PCs represents a step forward in our understanding of spatial cognition across species and the functional role of the early vertebrate telencephalon.

Characterization of Trabecular Bone Microarchitecture and Mechanical Properties Using Bone Surface Curvature Distributions.

Understanding bone surface curvatures is crucial for the advancement of bone material design, as these curvatures play a significant role in the mechanical behavior and functionality of bone structures. Previous studies have demonstrated that bone surface curvature distributions could be used to characterize bone geometry and have been proposed as key parameters for biomimetic microstructure design and optimization. However, understanding of how bone surface curvature distributions correlate with bone microstructure and mechanical properties remains limited. This study hypothesized that bone surface curvature distributions could be used to predict the microstructure as well as mechanical properties of trabecular bone. To test the hypothesis, a convolutional neural network (CNN) model was trained and validated to predict the histomorphometric parameters (e.g., BV/TV, BS, Tb.Th, DA, Conn.D, and SMI), geometric parameters (e.g., plate area PA, plate thickness PT, rod length RL, rod diameter RD, plate-to-plate nearest neighbor distance NNDPP, rod-to-rod nearest neighbor distance NNDRR, plate number PN, and rod number RN), as well as the apparent stiffness tensor of trabecular bone using various bone surface curvature distributions, including maximum principal curvature distribution, minimum principal curvature distribution, Gaussian curvature distribution, and mean curvature distribution. The results showed that the surface curvature distribution-based deep learning model achieved high fidelity in predicting the major histomorphometric parameters and geometric parameters as well as the stiffness tenor of trabecular bone, thus supporting the hypothesis of this study. The findings of this study underscore the importance of incorporating bone surface curvature analysis in the design of synthetic bone materials and implants.