Effects Of Spatial Heterogeneity Research Articles

Transient Absorption Microscopy Maps Spatial Heterogeneity and Distinct Chemical Environments in Photocatalytic Carbon Nitride Particles.

Limitations in solar energy conversion by photocatalysis typically stem from poor underlying charge carrier properties. Transient Absorption (TA) reveals insights on key photocatalytic properties such as charge carrier lifetimes and trapping. However, on the microsecond timescale, these measurements use relatively large probe sizes ranging in millimetres to centimetres which averages the effect of spatial heterogeneity at smaller length scales. A home-built Transient Absorption Microscopy (TAM) setup is reported and used to study single particles of carbon nitride (CNx), an emerging photocatalyst. For the first time, to the best of the authors' knowledge, µs-s timescales are explored within individual particles to gain a more complete understanding of their photophysics. The dynamics of trapped charges are monitored, enabling measurement and quantification of heterogeneity in the transient absorptance signal of individual CNx particles and within them. Particle-to-particle heterogeneity in the trapped charge density is observed, while spatial heterogeneity in lifetimes within a particle is revealed using a smaller probe beam with a ≈5µm diameter. Overall, the observations suggest that contributions from different local environments independently influence charge trapping at different timescales. TAM on the micron and microsecond spatiotemporal resolution will aid in tackling design questions about optimal chemical environments for the promotion of photoactivity.

Integrating variable importance and spatial heterogeneity to reveal the environmental effects on outdoor jogging

Outdoor jogging is increasingly recognized as a crucial component of urban active transport strategies aimed at improving public health. Despite growing research on the influence of both natural and built environmental factors on outdoor jogging, less is known about the relative importance of these factors. Moreover, the spatial heterogeneity effects of environmental factors remain unclear. Failing to consider these varying effects regarding impact intensity and spatial scale results in inefficient planning policies aimed at promoting active transport. This study addresses these gaps by analyzing crowdsourced jogging trajectory data in Shenzhen using a computational framework that combines Random Forest Variable Importance (RF-VI) and Multi-Scale Geographically Weighted Regression (MGWR). The analysis identifies hierarchical environmental effects and the varying impacts of twelve key determinants across different spatial scales. Results reveal that natural environmental factors are most contributing to outdoor jogging, while density-related built environment factors contribute the least. Additionally, environmental effects vary in scale, direction, and intensity, with seven variables exerting global impacts and five showing localized effects. Notably, the central and suburban areas of Shenzhen display considerable spatial heterogeneity in environmental influences. The findings inform the importance of integrating green infrastructure, mitigating over-dense urban development, and enhancing pedestrian-accessible road networks to promote outdoor jogging. These insights advocate for context-sensitive urban planning that balances natural and built environments to to foster healthier mobility.

Effect of Spatial Heterogeneity on the Elasticity and Fracture of Polymer Networks

Effect of Spatial Heterogeneity on the Elasticity and Fracture of Polymer Networks

Regional dynamic hazard assessment of rainfall–induced landslide guided by geographic similarity

Landslides triggered by rainfall are complex phenomena influenced by a multitude of condition and trigger factors. A significant challenge in the field is the accurate and interpretable assessment of large-scale landslide hazards, particularly due to the lack of consideration for the synergistic effects of multiple triggers and spatial heterogeneity. This study introduces a novel regional hazard assessment method that leverages geographic similarity to address these challenges. Our approach consists of four key steps: (1) extraction of sample information from relevant data based on the historical distribution of landslides and their influencing factors, (2) application of a scale-space algorithm to manage spatial heterogeneity, with a partition scale determined by the q-value variation, (3) optimization of sample configuration and generation criteria under the guidance of geographic similarity for enhanced spatiotemporal modeling, and (4) utilization of machine learning models to refine inductive bias and capture nonlinear relationships, enabling a quantitative estimation of hazard probabilities for each slope unit within the prediction module. We applied our P-RF + method to Yunnan Province, China, incorporating 11 condition factors and 7 trigger factors across 624 historical rainfall-induced landslides and 1248 non-landslide cases. Comparative experiments reveal that the P-RF + model substantially outperforms existing methods in accuracy and interpretability. Furthermore, a case study during the rainy season illustrates the model's capability to provide timely warning instructions for rainfall-induced landslides. These findings underscore the potential of our proposed method to offer valuable insights for disaster prevention decision-making.Graphical

Impact of Paddy Field Expansion on Ecosystem Services and Associated Trade-Offs and Synergies in Sanjiang Plain

In recent decades, the integrity and security of the ecosystem in the Sanjiang Plain have faced severe challenges due to land reclamation. Understanding the impact of paddy field expansion on regional ecosystem services (ESs), as well as revealing the trade-offs and synergies (TOS) between these services to achieve optimal resource allocation, has become an urgent issue to address. This study employs the InVEST model to map the spatial and temporal dynamics of five key ESs, while the Optimal Parameter Geodetector (OPGD) identifies primary drivers of these changes. Correlation analysis and Geographically Weighted Regression (GWR) reveal intricate TOS among ESs at multiple scales. Additionally, the Partial Least Squares-Structural Equation Model (PLS-SEM) elucidates the direct impacts of paddy field expansion on ESs. The main findings include the following: (1) The paddy field area in the Sanjiang Plain increased from 5775 km2 to 18,773.41 km2 from 1990 to 2020, an increase of 12,998.41 km2 in 40 years. And the area of other land use types has generally decreased. (2) Overall, ESs showed a recovery trend, with carbon storage (CS) and habitat quality (HQ) initially decreasing but later improving, and consistent increases were observed in soil conservation, water yield (WY), and food production (FP). Paddy fields, drylands, forests, and wetlands were the main ES providers, with soil type, topography, and NDVI emerging as the main influencing factors. (3) Distinct correlations among ESs, where CS shows synergies with HQ and SC, while trade-offs are noted between CS and both WY and FP. These TOS demonstrate significant spatial heterogeneity and scale effects across subregions. (4) Paddy field expansion enhances regional SC, WY, and FP, but negatively affects CS and HQ. These insights offer a scientific basis for harmonizing agricultural development with ecological conservation, enriching our understanding of ES interrelationships, and guiding sustainable ecosystem management and policymaking.

Significant negative impact of human activities on carbon storage in the Yellow River Delta over the past three decades

With the increasing intensification of human activities, significant changes in land use and land cover (LULC) have posed a severe threat to the carbon storage capacity of wetland ecosystems. A deep understanding of this impact is crucial for protecting regional ecosystems and promoting sustainable development. This study utilized the Integrated Valuation of Ecosystem Services and Tradeoffs (InVEST) model and the human activity intensity (HAI) index to conduct detailed grid analysis and global analysis of carbon storage through creating fishnet system and explored the complex relationship between carbon storage and HAI in the Yellow River Delta (YRD), China. The results indicated that over the past 30 years, natural wetlands such as meadow wetlands and salt marshes in the study area had undergone significant degradation due to escalating human activities, while artificial wetlands and non-wetland areas expanded. Concurrently, the total regional carbon storage had declined by 2.08 Tg, representing a significant drop of 8.22 % in the YRD from 1990 to 2020. Among them, dry land, as the primary land type, served as the most crucial carbon pool. Additionally, the human activity intensity of land surface (HAILS) increased significantly, with a growth rate of 37.27 %. HAI mapping revealed a continuous expansion of areas with high HAI. In contrast, the Yellow River Delta National Nature Reserve (YRDNNR) maintained relatively low HAI. Correlation analysis further showed the significant negative correlation (p < 0.01) between carbon storage and HAI, with r values of grid analysis ranging from −0.1395 to −0.0334, while that for global analysis was −0.9643, respectively. This reflected the spatial heterogeneity and agglomeration effects of data analysis across different scales. This study provides valuable insights for achieving the “dual carbon” goals and supporting the conservation and management of wetland ecosystems.

Driving factors of phytoplankton Reynolds functional groups (RFGs) in a subtropical reservoir (São Paulo, Brazil)

Subtropical reservoirs are susceptible to the eutrophication process, largely due to inappropriate land use and occupation in the watersheds, resulting in changes in the composition of the phytoplankton community, according to the sensitivity and environmental tolerances of the different species. Application of the Reynolds functional groups (RFGs) method to the multispecies phytoplankton community is a valuable approach that can be used to answer ecological questions at different spatial and temporal scales. The Itupararanga reservoir, in the upper Sorocaba River basin (São Paulo state, Brazil), is used to supply drinking water to approximately one million people, as well as for agricultural and recreational purposes. This study examines the relationships between environmental variables and the composition of the phytoplankton community, identifying the main functional groups (RFGs) along a spatial gradient in the reservoir (from upstream to downstream), during one year. Five samplings were performed at seven points in the reservoir, in the rainy and dry seasons (from 2016 to 2017). The effects of spatial heterogeneity influenced the formation of different biomass gradients for each functional group. The most abundant RFGs were Sn (warm mixed environments), H1 (eutrophic, both stratified and shallow lakes with low nitrogen content), and Lo (deep and shallow, oligotrophic to eutrophic, medium to large lakes), which corresponded to the spatial heterogeneity of the reservoir. The variables with the greatest influence on the phytoplankton composition in the reservoir were total nitrogen, nitrite, and the N/P ratio, with phosphorus as the limiting nutrient. The presence of Cyanobacteria (codons Sn and H1) was driven by the stability of the water column, due to the long residence time of the water in the reservoir. This research demonstrated the effectiveness of using RFGs as environmental descriptors, providing an essential tool in aquatic ecology studies.

Spatial heterogeneity and interaction effect of urban blue and green spaces on housing prices

Rapid urbanization presents policymakers and planners with the challenge of balancing public open spaces design with the conservation and improvement of natural resources. A comprehensive understanding of the land economic value of urban blue-green spaces (UBGS) holds immense significance for urban sustainable development, urban spatial justice and the promotion of human well-being. In this study, the MGWR model is employed to discuss the heterogeneous effects of UBGS on housing prices in Hangzhou. Additionally, the interaction effect between blue space and green space was examined at the district level, and the specific locations and spatial patterns were identified. The results show that (1) different types, features and accessibility of UBGS have different degrees and spatial scale of effect on housing prices, and will be affected by other attributes of UBGS; (2) in 30.92% of the main urban area of Hangzhou, the effect of blue spaces and green spaces on housing prices exhibits an interactive effect. The spatial patterns are divided into blue-green positive synergistic, antagonistic and negative synergistic regions; (3) green space has positive and negative effects on housing prices, while blue space has positive effects on housing prices at the regional level. The existence of water bodies can promote the positive effect of green spaces on housing prices or alleviate the negative effect. The results indicate that planners must transcend the singular focus on blue or green space planning and instead consider both in an integrated manner. This outcome can provide valuable references for UBGS planning.

Three-dimensional numerical modeling of soil-roots system based on X-ray computed tomography: Hydraulic effects study

Vegetation roots enhance soil stability by influencing saturation and pore structure, playing a pivotal role in stabilizing slopes, reducing erosion, and enhancing soil structure. However, current research on the hydraulic effects of roots on soil remains relatively limited. The micro-mechanisms of vegetation's impact on soil and the macro-level connections are not yet fully understood, which poses a challenge to the modeling of root-soil system. This study develops a three-dimensional (3D) finite element model of root-soil composites based on root computed tomography (CT) images and experimental results. Four different groups are modeled, including the rootless group, and those with Festuca arundinacea (FA) roots at various growth stages. The simulation results show that the saturation in the shallow layers significantly decreases in root-soil composite groups, and the rhizosphere water content is lower than that away from the roots, resulting in a net water flux toward the roots. The influence range of roots on suction is gradually amplified with increasing root growth process and root water uptake time. Higher levels of root development result in a stronger overall water uptake effect, leading to a more pronounced decrease in saturation. Closer proximity to the surface roots results in a more rapid increase in soil suction. Compared with one-dimensional root water uptake models, this model considers the effects of spatial heterogeneity of root structures on soil, which provides a comprehensive modeling basis for studying the effect of root system on soil.

Stochastic hazard assessment framework of landslide blocking river by depth-integrated continuum method and random field theory

Landslide-induced barrier dams pose a threat to the safety of humans, livestock and nearby infrastructures. The efficient assessment of landslide blocking river is crucial for disaster prevention and mitigation solutions. This study proposes a novel stochastic assessment framework to evaluate the landslide blocking river through the prediction of their deposition depths and considering the heterogeneity of shear strength parameters on the potential sliding surface. The depth-integrated continuum method (DICM) is used to simulate the landslide runout process. Using an enhanced Karhunen-Loève expansion (KLE) method, the spatial variations in soil's shear strength parameters are modeled by random fields to incorporate the effects of soil's spatial heterogeneity on the landslide deposition pattern. Subsequently, the multi-response surrogate model is constructed to relate the random field variables to the deposition depths based on extreme gradient boosting (XGBoost). To improve the performance of the surrogate model, principal component analysis (PCA) and sliced inverse regression (SIR) methods are employed for the dimension reduction of output and input variables, respectively. Furthermore, the algorithm for river blockage identification is developed to search for the deposition ridges. To demonstrate the capability of the stochastic assessment framework, an example of the first Baige landslide in Tibet, China is simulated, and the affected region and deposition depths of the landslide are predicted to calculate the probability of river damming. The presented methodology provides a practical means for improving the landslide blocking river prediction and new insights for early warning and risk mitigation.

The green trade benefits and horizontal ecological compensation from the perspective of embodied carbon emissions: A case study of the Yellow River Basin, China

The horizontal ecological compensation plays an important role in balancing the interests of all parties and coordinating regional development in the basin. However, the mechanism of ecological compensation based on embodied carbon emissions is still poorly understood. Here, taking the Yellow River Basin as the research area, we use the multi-regional input-output (MRIO) model to measure the embodied carbon transfers between its seven urban agglomerations in 2012 and 2017 from the viewpoint of value-added trade benefits. Further, for the first time, the green trade benefits and ecological compensation amounts are analyzed. The results indicate that: (1) The transfer of trade-embodied carbon among the urban agglomerations in the basin showed obvious spatial heterogeneity and geographic proximity effects, and trade-embodied carbon outflows (inflows) had a pattern of "highest in the midstream, second in the downstream, and lowest in the upstream". (2) The industry composition of the urban agglomerations in relation to embodied carbon outflows (inflows) was similar, mainly in the service and heavy manufacturing industries. (3) The spatial pattern of green trade benefits in the basin had shifted from "high in the north and low in the surrounding area" to "high in the east-central part and low in the west". (4) The pattern of ecological compensation in the basin had shifted from the upstream surplus, the middle and downstream deficit to the midstream deficit, and the upstream and downstream surplus. Therefore, we recommend improving energy structures in high-demand urban agglomerations by adopting clean energy, focusing on decarbonization and energy efficiency in resource-rich regions. Additionally, promoting low-carbon economies, especially in the service and heavy manufacturing industries, implementing differentiated emission reduction strategies, and optimizing carbon compensation mechanisms considering regional disparities and resource endowments are crucial. It is expected that the study can enrich the scientific basis of horizontal ecological compensation and increase the fairness of regional carbon emission rights allocation.

Application of non-stationary shear-wave velocity randomization approach to predict 1D seismic site response and its variability at two downhole array recordings

Accounting for uncertainties in seismic site response is crucial to improving the performance of one-dimensional (1D) ground response analyses (GRAs) at downhole array recording sites. In addition to site effects, uncertainties in 1D-GRAs can also be contributed from the seismic source and/or path. Though often representing not more than one percent of the distance (path) from the source, site conditions are known to have an enormous influence on ground shaking. In this study, we focus on the site shear-wave velocity (VS) structure, which is the main ingredient for estimating the variability of site response. As such, VS can manifest aleatory uncertainties related to the effects of small-scale spatial heterogeneities within the near surface, thus VS can substantially modify ground shaking during earthquakes. We apply a novel VS randomization approach to propagate the small-scale heterogeneities of VS to estimate seismic site response within a non-stationary probabilistic framework. The randomization approach generates samples of VS profiles that are used to perform several 1D-GRAs and obtain an averaged site response and related variability. The proposed method is implemented on data recorded at two downhole array sites with different subsurface soil conditions: a soft soil site on Treasure Island (California, United States of America) and a rock outcrop site in Cadarache (South-East France). We show that synthetic surface-to-borehole transfer functions from 1D-GRAs provide an acceptable fit to the empirical transfer functions from low-motion earthquake records and succeed in reproducing most of the site-specific seismic response variability. The remaining mismatch between transfer functions is likely due to insufficient precision on the seismic bedrock and the impedance contrast. The variability in site response is discussed with emphasis on the role of VS small-scale heterogeneities, attenuation, and input motion incidence angle in ground motion variability for the site and soil conditions at both locations.

Analysis of multi-scale effects and spatial heterogeneity of environmental factors influencing purse seine tuna fishing activities in the Western and Central Pacific Ocean

Understanding the spatial fishing activity distribution characteristics is important for the sustainable development of fisheries. Spatial nonstationarity is always present, especially in marine ecosystems. To explore how marine environmental factors affect the fishing effort of tuna purse seine vessels, data from 2015 to 2020 on the fishing activities of these fleets and environmental variables in the Western and Central Pacific Ocean (WCPO) were analyzed. A Generalized Additive Model (GAM), Geographically Weighted Regression model (GWR), and Multi-Scale Geographically Weighted Regression (MGWR) model were applied to explore the drivers of fishing activity and the impacts of environmental factors on spatial heterogeneity. The results indicate that: (1) The MGWR models has the highest prediction accuracy and effectively reflects the spatial heterogeneity and multi-scale effects of environmental factors in a year. (2) Environmental factors exhibit significant multi-scale effects and spatial heterogeneity on the fishing activities of purse seine tuna vessels. Sea floor depth, salinity at 200 m depth and sea surface temperature show the greatest spatial heterogeneity in their impact on fishing activities. (3) Sea surface temperature, distance to port, and primary productivity and salinity at 200 m depth are key variables influencing the fishing activities of purse seine tuna vessels. These findings are expected to provide scientific and effective guidance for fishery management and sustainable development by assessing the spatial variations in fishing activities at multiple scales.

A multiscale and multiperspective quantifying framework for spatial patterns and influencing mechanisms of geographical indications

Geographical indications (GIs) embody distinctive regional elements characterized by widespread spatial distribution, serving as vital agricultural intellectual properties and significant tourism assets. This case study introduces a multiscale and multi-perspective quantification framework for Shandong Province, focusing on spatial agglomeration, association, and heterogeneity. This approach quantitatively explores GIs’ spatial patterns and influencing mechanisms, analyzing both at the monomer and regional scales, considering static and dynamic perspectives. Leveraging methods such as kernel density analysis, Moran’s I index, Geary’s C index, Internet hot word analysis, and Geodetector, the coastal municipalities, prosperous urban areas, and zones with high-quality arable soils were identified as spatial agglomeration areas for GIs. The study revealed a strong correlation between the spatial distribution pattern of socioeconomic factors and GIs’ spatial density from a static perspective. However, diminished spatial autocorrelation was observed for GIs’ public perception from a dynamic standpoint, indicating a reduced influence of Internet connectivity. The spatial heterogeneity in GIs is determined by multiple interconnected factors, displaying an enhancement effect between any two influencing factors. Among the 15 influencing factors analyzed, urbanization rate; gross value of agricultural, forestry, animal husbandry, and fishery production; and per capita gross domestic product significantly contribute to spatial heterogeneity effects at both urbanization rate, gross value of agriculture, forestry, animal husbandry, fishery production, and per capita gross domestic product significantly contributed to spatial heterogeneity effects at regional and monomer scales. The results suggest that GIs are likely to flourish with regional economic growth. The analytical framework and quantification methods support exploring and sustainably utilizing GIs, improving output quality, and modernizing GIs’ production, ultimately contributing to regional agriculture’s high-quality and sustainable development.

Spatial analysis of the impact of urban built environment on cardiovascular diseases: a case study in Xixiangtang, China

BackgroundThe built environment, as a critical factor influencing residents' cardiovascular health, has a significant potential impact on the incidence of cardiovascular diseases (CVDs).MethodsTaking Xixiangtang District in Nanning City, Guangxi Zhuang Autonomous Region of China as a case study, we utilized the geographic location information of CVD patients, detailed road network data, and urban points of interest (POI) data. Kernel density estimation (KDE) and spatial autocorrelation analysis were specifically employed to identify the spatial distribution patterns, spatial clustering, and spatial correlations of built environment elements and diseases. The GeoDetector method (GDM) was used to assess the impact of environmental factors on diseases, and geographically weighted regression (GWR) analysis was adopted to reveal the spatial heterogeneity effect of environmental factors on CVD risk.ResultsThe results indicate that the built environment elements and CVDs samples exhibit significant clustering characteristics in their spatial distribution, with a positive correlation between the distribution density of environmental elements and the incidence of CVDs (Moran’s I > 0, p < 0.01). Further factor detection revealed that the distribution of healthcare facilities had the most significant impact on CVDs (q = 0.532, p < 0.01), followed by shopping and consumption (q = 0.493, p < 0.01), dining (q = 0.433, p < 0.01), and transportation facilities (q = 0.423, p < 0.01), while the impact of parks and squares (q = 0.174, p < 0.01) and road networks (q = 0.159, p < 0.01) was relatively smaller. Additionally, the interaction between different built environment elements exhibited a bi-factor enhancement effect on CVDs. In the local analysis, the spatial heterogeneity of different built environment elements on CVDs further revealed the regional differences and complexities.ConclusionsThe spatial distribution of built environment elements is significantly correlated with CVDs to varying degrees and impacts differently across regions, underscoring the importance of the built environment on cardiovascular health. When planning and improving urban environments, elements and areas that have a more significant impact on CVDs should be given priority consideration.

Attributing spatially stratified heterogeneity in biodiversity of urban–rural interlaced zones based on the OPGD model

Urban–rural interlaced zones are characterized by the interpenetration of urban and rural elements, drastic changes in construction, relatively weak planning and management, and anthropogenic activities that constantly impact the ecological background. However, the ecological barriers and hinterland spaces of the city center provide important ecological functions. In this study, we selected forest birds as indicator species of the urban ecological environment and explored the spatial stratification and heterogeneity effects of environmental substrates and anthropogenic activities on bird diversity (species richness, abundance, Shannon–Wiener index, and Simpson index) in urban–rural interlaced zones using the optimal parameter geographic detector model to characterize the changes in ecological functions in these zones. The results of this study are as follows:(1) The bird diversity index in Minhang District, Shanghai, showed an obvious urban-rural gradient divergence with the transition of urban zone- rural-urban interface - rural zone.An agglomerative spatial differentiation pattern was observed more in the southeast but less in the northwest, with a high degree of spatial distribution concentrations and evident imbalance characteristics.(2) The spatially stratified heterogeneity in bird diversity in urban–rural interlaced zones was because of the combined action of multiple driving factors under the three dimensions of habitat environment, degree of urbanization, and anthropogenic interference. Most of the interactions between any two factors showed non-linear or bifactorial enhancement effects. Furthermore, the one-factor explanatory power of urbanization and anthropogenic interference factors on bird diversity was significantly higher than that of the habitat environment factor.(3) Population heat distribution (PD), distance to the center of Shanghai (DC), and nighttime lighting index(NTL) were the main drivers of spatially stratified heterogeneity in bird diversity and the key indicators of urban–rural gradient changes. The interaction between PD and DC had the strongest explanatory power for the spatial differentiation of bird diversity.

The non-linear impact of urban rail transit on commercial property prices: Based on a spatial heterogeneity perspective

Urban rail transit (URT) can boost population and business agglomeration, and increase premiums for surrounding properties. Commercial properties with an operational nature typically gain higher premiums and have the potential to capture value. However, the relationship between URT and commercial property price (CPP) has not been fully explored. Therefore, this paper takes Shanghai as an example, based on URT travel data, property sales information, and other multi-source geographic data, comprehensively analyses the intrinsic mechanism of URTs affecting CPPs. The results confirm that URTs have a significant positive effect on CPPs, but the degree of impact varies in the presence of spatial heterogeneity and submarket effects. On the urban scale, the effect increases and then decreases as one moves away from the CBD; at the station area scale, URTs have a non-linear step-decreasing effect on CPPs. Furthermore, the premium that URTs can generate is limited and subject to multiple constraints in terms of location, built environment, residents' travel habits and expectations. The findings can provide a reference for formulating value capture policy, planning URT routes, and enhancing urban economic vitality.

Spatial clustering based on geographically weighted multivariate generalized gamma regression

Geographically Weighted Regression (GWR) is one of the local statistical models that can capture the effects of spatial heterogeneity. This model can be used for both univariate and multivariate responses. However, it should be noted that GWR models require the assumption of error normality. To overcome this problem, we propose a GWR model for generalized gamma distributed responses that can capture the phenomenon of some special continuous distributions. The proposed model is known as Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR). Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method optimized with the Bernt-Hall-Hall-Haussman (BHHH) algorithm. To determine the significance of the spatial heterogeneity effect, a hypothesis test was conducted using the Maximum Likelihood Ratio Test (MLRT) approach. We made a spatial cluster based on the estimated model parameters for each response using the k-means clustering method to interpret the obtained results. Some highlights of the proposed method are:•A new model for GWR with multivariate generalized gamma distributed responses to overcome the assumption of normally distributed errors.•Goodness of fit test to test the spatial effects in GWMGGR model.•Spatial clustering of districts/cities in Central Java based on three dimensions of educational indicators.

ROBUST GEOGRAPHICALLY WEIGHTED REGRESSION WITH LEAST ABSOLUTE DEVIATION (LAD) ESTIMATION AND M-ESTIMATION ON GRDP OF WEST JAVA PROVINCE

Geographically Weighted Regression (GWR) is an analytical method for data that contains spatial heterogeneity effects. However, parameter estimation in the GWR model has a weakness, namely it is prone to outliers and can cause the parameter estimation to be biased. This can be overcome by the Robust Geographically Weighted Regression (RGWR) method which is more robust against the presence of outliers. This method is suitable for Gross Regional Domestic Product (GRDP) data in West Java Province, which contains outliers and also has spatial effects. The data used in this study are secondary data obtained from the Central Statistics Agency (BPS) of West Java Province. The purpose of this study is to compare the Robust Geographically Weighted Regression (RGWR) method with the Least Absolute Deviation (LAD) Estimation and M-estimation and also to find out the factors that affect the Gross Regional Domestic Product (GRDP) in West Java Province in 2021 based on the model resulting from. Selection of the best model is seen based on the value of the coefficient of determination (R2) and Mean Squared of Error (MSE). The research results show that the Robust Geographically Weighted Regression (RGWR) method with M-estimation is much more effective in estimating the distribution of GRDP in West Java Province in 2021, seen from the larger coefficient of determination and the smaller Mean Square Error (MSE). The variables that have a significant influence on GRDP in West Java Province in 2021 are the variables of foreign investment and local income.

Modelling the effects of void swelling and spatial heterogeneity on the fracture of metallic materials by crystal plasticity

To theoretically analyse how void swelling and spatial heterogeneity impact the fracture behaviour of metallic materials, a coupled porous crystal plasticity framework has been developed. The proposed framework is then applied to analyse the fracture behaviour of metallic materials under different swelling conditions and types of spatial heterogeneity. It is revealed that at low porosity, the spatial heterogeneity of voids will have limited influence on the fracture behaviour of the material. However, at high porosity, owing to void swelling, a concentrated distribution of voids near grain boundaries can lead to a strong deformation localization, which can be seen as an indicator of possible quasi-brittle fracture. It is further discovered that the inner pressure of the voids tends to reduce the yield stress of the material and promote localized plastic deformation. As a result, such pressure will enhance the impact of concentrated distribution of voids, which can lead to further embrittlement of the material. The present study reveals the key role of void swelling and spatial heterogeneity in regulating the fracture behaviour of metallic materials, a step towards a better understanding over the failure mechanisms of metallic materials under extreme conditions.