Cross K-function Research Articles

Quantitative Modeling to Characterize Maternal Inflammatory Response of Histologic Chorioamnionitis in Placental Membranes.

The placental membranes are a key barrier to fetal and uterine infection. Inflammation of the membranes, diagnosed as maternal inflammatory response (MIR) or alternatively as acute chorioamnionitis, is associated with adverse maternal-fetal outcomes. MIR is staged 1-3, with higher stages indicating more hazardous inflammation. However, the diagnosis relies upon subjective evaluation and has not been deeply characterized. The goal of this work is to develop a cell classifier for eight placental membrane cells and quantitatively characterize MIR1-2. Hematoxylin and eosin (H&E)-stained placental membrane slides were digitized. A convolutional neural network was trained on a dataset of hand-annotated and machine learning-identified cells. Overall cell class-level metrics were calculated. The model was applied to 20 control, 20 MIR1, and 23 MIR2 placental membrane cases. MIR cell composition and neutrophil distribution were assessed via density and Ripley's cross K-function. Clinical data were compared to neutrophil density and distribution. The classification model achieved a test-set accuracy of 0.845, with high precision and recall for amniocytes, decidual cells, endothelial cells, and trophoblasts. Using this model to classify 53073 cells from healthy and MIR1-2 placental membranes, we found that (1) MIR1-2 have higher neutrophil density and fewer decidual cells and trophoblasts, (2) Neutrophils colocalize heavily around decidual cells in healthy placental membranes and around trophoblasts in MIR1, (3) Neutrophil density impacts distribution in MIR, and (4) Neutrophil metrics correlate with features of clinical chorioamnionitis. This paper introduces cell classification into the placental membranes and quantifies cell composition and neutrophil spatial distributions in MIR.

Enhancing bivariate spatial association analysis of network-constrained geographical flows: An incremental scale-based method

Measuring bivariate spatial association plays a key role in understanding the spatial relationships between two types of geographical flow (hereafter referred to as “flow”). However, existing studies usually use multiple scales to analyze bivariate associations of flows, leading to the results at larger scales can be strongly affected by the results at smaller scales. Moreover, the planar space assumption of most existing studies is unsuitable for network-constrained flows. To solve these problems, a network incremental flow cross K-function (NIFK) is developed in this study by extending the cross K-function for points into a flow context. Specifically, two versions of NIFK were developed in this study: the global version to check whether bivariate associations exist in the whole study area and the local version to identify specific locations where associations occur. Experiments on three simulated datasets demonstrate the advantages of the proposed method over an available alternative method. A case study conducted using Xiamen taxi and ride-hailing service datasets demonstrates the usefulness of the proposed method. The detected bivariate spatial association provides deep insights for understanding the competition between taxi services and ride-hailing services.

Exploring spatial associations between near-miss and police-reported crashes: The Heinrich’s law in traffic safety

This research explores the spatial association between police-reported crashes and near-miss crashes experienced by community members using the network cross K-function method and Geographic Information Systems (GIS). The near-miss crashes were collected from a field survey conducted in Seoul, South Korea, and police-reported crashes in the study area were also collected for comparison. The results show that minor and severe police-reported crashes have statistically significant spatial associations, and near-miss and police-reported crashes also have significant associations. Thus, the Heinrich’s law, which postulates that police-reported minor and severe crashes and near-miss crashes may share underlying locational factors, has merit to apply in traffic safety. These findings indicate that road users’ near-miss crash experiences reflecting local knowledge can supplement police-reported traffic crashes to identifying crash hotspots in road networks and developing safety improvement measures and strategies.

CD8 + T cell infiltration is associated with improved survival and negatively correlates with hypoxia in clear cell ovarian cancer

Unlike other histological types of epithelial ovarian carcinoma, clear cell ovarian carcinoma (CCOC) has poor response to therapy. In many other carcinomas, expression of the hypoxia-related enzyme Carbonic anhydrase IX (CAIX) by cancer cells is associated with poor prognosis, while the presence of CD8 + tumor-infiltrating lymphocytes (TIL) is positively prognostic. We employed [18F]EF5-PET/CT imaging, transcriptome profiling, and spatially-resolved histological analysis to evaluate relationships between CAIX, CD8, and survival in CCOC. Tissue microarrays (TMAs) were evaluated for 218 cases in the Canadian COEUR study. Non-spatial relationships between CAIX and CD8 were investigated using Spearman rank correlation, negative binomial regression and gene set enrichment analysis. Spatial relationships at the cell level were investigated using the cross K-function. Survival analysis was used to assess the relationship of CAIX and CD8 with patient survival for 154 cases. CD8 + T cell infiltration positively predicted survival with estimated hazard ratio 0.974 (95% CI 0.950, 1000). The negative binomial regression analysis found a strong TMA effect (p-value < 0.0001). It also indicated a negative association between CD8 and CAIX overall (p-value = 0.0171) and in stroma (p-value = 0.0050) but not in tumor (p-value = 0.173). Examination of the spatial association between the locations of CD8 + T cells and CAIX cells found a significant amount of heterogeneity in the first TMA, while in the second TMA there was a clear signal indicating negative spatial association in stromal regions. These results suggest that hypoxia may contribute to immune exclusion, primarily mediated by effects in stroma.

Geographically Weighted Flow Cross K-Function for Network-Constrained Flow Data

Network-constrained spatial flows are usually used to describe movements between two spatial places on a road network. The analysis of the spatial associations between different types of network-constrained spatial flows plays a key role in understanding the spatial relationships among different movements. However, existing studies usually do not consider the effect of distance decay, which may reduce the effectiveness of the detected bivariate spatial flow patterns. Moreover, most existing studies are based on the planar space assumption, which is not suitable for network-constrained spatial flows. To overcome these problems, this study proposed a new statistical method, the Geographically Weighted Network Flow Cross K-function, which improves the Flow Cross K-Function method by taking the distance decay effect and the constraints of road networks into account. Both global and local versions are extended in this study: the global version measures the overall spatial association and the local version identifies the exact locations where a spatial association occurs. The experiments on simulated datasets show that the proposed method can identify predefined bivariate flow patterns. In a case study, the proposed method is also applied to flow data comprising Xiamen taxi and ride-hailing datasets. The results demonstrate that the proposed method effectively identifies the competitive relationships between taxi and ride-hailing services.

Examining Time-Variant Spatial Dependence of Urban Places and Shootings.

Place-based interventions are increasingly implemented to address firearm violence. While research on the social determinants of health and criminological theories suggest that the built environment significantly influences health outcomes and the spatial distribution of crime, little is known about the attraction between urban places and shootings. The present study adds to the literature on firearm violence and micro-place research by exploring the spatial dependence in a Midwest metropolitan area between shootings and bus stops, vacant properties, alcohol outlets, and other locations that have been theoretically or empirically linked to firearm violence. The G-function and Cross-K function are used to characterize the univariate clustering of shootings and bivariate attraction with other locations, respectively. Bus stops, blighted vacant properties, alcohol outlets, and businesses/residential locations participating in a public-private-community initiative to reduce crime exhibited significant locational dependence with shootings at short distances. Attraction between on-premises alcohol outlets and shootings was observed only during the night. No attraction was found between schools and shootings. The findings reaffirm the importance of place-based research-especially at the micro-place level-and suggest that certain urban places may be appropriate targets for interventions that modify existing physical and/or social structures.

Hand, Foot and Mouth Disease (HFMD): Prevalence and its Spatial Relationship with Vaccine Refusal Cases in Terengganu, Malaysia

Hand, foot and mouth disease (HFMD) is a global public health problem with pandemic potential. The progressive increment of HFMD cases in Malaysia needs further investigation to identify the pattern of disease spread, including its proximity to vaccine refusal. We sought to estimate the prevalence of HFMD in Terengganu and determine the spatial relationship between HFMD and vaccine refusal cases. This study employed data from the national electronic communicable disease notification system and vaccine refusal database maintained by the Communicable Disease Control (CDC) Unit and Maternal and Child Health Care (MCH) Unit. Data from all cases recorded in 2016 were provided by the Terengganu State Health Department, Malaysia. The number of HFMD cases for each district was estimated using the points-in-polygons function in R software. The spatial relationship between HFMD cases and vaccine refusal cases was tested using the cross K-function test. A total of 811 HFMD cases was notified in 2016, with the overall prevalence at 80.2 cases per 100,000 population. Among all districts in Terengganu, the prevalence of HFMD ranged from 19.2 to 230.9 cases per 100,000 population, with the cases highly concentrated in three districts: Kuala Terengganu, Marang, and Dungun. There was evidence of a spatial cluster of HFMD cases based on the Nearest Neighbour Index, r = 0.27 (p-value &lt; 0.01). Moreover, the locations of HFMD cases were statistically and closely related to the areas of vaccine refusal cases (cross K test, p-value &lt; 0.010). The prevalence of HFMD from year to year was high. HFMD cases and vaccine refusal cases formed clusters in the districts with a high-density population. The proximity of HFMD cases and vaccine refusal cases in Terengganu warrants further investigation.

Network constrained and classified spatial pattern analysis of healthcare facilities and their relationship with the road structure: a case study of Thiruvananthapuram city

Equity of the utilization of medical facilities is extremely dependant on the spatial distribution of healthcare amenities. In this study, an attempt is made to study the geographic distribution of the various categories of healthcare facilities in the city of Thiruvananthapuram, South India using the centrographic analysis that includes the Mean Center, Standard Deviational Ellipse and Average Nearest Neighbour and it was found that there is an uneven distribution. Network-based point pattern analysis is also performed and cross k-function is used to determine the distribution of medical shops relative to the healthcare services. A weighted node approach is used to calculate the indices of centrality by weighing all nodes based on their degree using Geographical Information System (GIS). Multi centrality assessment model consisting of betweenness, closeness and straightness centrality is used to compute the weighted road centrality on a local and global scale. Kernel Density Estimation technique is applied to modify the centrality values and the vector points to a basic raster framework. Correlation analysis was performed to find the role of the network centrality on the location of healthcare facilities in the study area. Correlation values are greatest among category 2 hospitals; straightness centrality and betweenness centrality favours the location of category 1 hospitals and homeopathy hospitals respectively. The results confirm that network topology influences the location of medical facilities in the study area.

The Spread of Rabies Among Dogs in Pranburi District, Thailand: A Metapopulation Modeling Approach

Rabies, a deadly zoonotic disease, is causing serious public health problems worldwide. Dogs are considered the main reservoir for rabies infection in humans. A better understanding of the dissemination of rabies in the dog population is crucial. The present study, therefore, aimed to explore the subpopulation of dogs roaming around rabies-outbreak areas and the model of its possible spread. We used a Cross-K function to investigate the spatial clustering between the locations of dog rabies cases and the feeding points of a stray dog feeder. We then observed the social interaction of dogs in a community using a metapopulation analysis and further simulated the possible spread of rabies within this population. We found that the reported rabies cases were spatially clustered with the routes of the dog feeder. Therefore, more sustainable stray dog management is required. Based on our community dog observations, we found 20 groups comprising 222 dogs with an average of 11 dogs per group. In our infectious model, we suggested that 47.7% of dogs are likely to be infected in a year if no interventions are implemented. Therefore, the veterinary authorities should rigorously strengthen their rabies prevention and control strategies to protect both animal and human health.

Revisiting the random shift approach for testing in spatial statistics

We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become the standard method for testing the independent superposition hypothesis in spatial statistics, and it is widely used in a plethora of practical applications. However, this method has a problem of liberality caused by breaking the marginal spatial correlation structure due to the toroidal correction. This indeed means that the assumption of exchangeability, which is essential for the Monte Carlo test to be exact, is not fulfilled.We present a number of permutation strategies and show that the random shift with the variance correction brings a suitable improvement compared to the torus correction in the random field case. It reduces the liberality and achieves the largest power from all investigated variants. To obtain the variance for the variance correction method, several approaches were studied. The best results were achieved, for the sample covariance as the test statistics, with the correction factor 1∕n. This corresponds to the asymptotic order of the variance of the test statistics.In the point process case, the problem of deviations from exchangeability is far more complex and we propose an alternative strategy based on the mean cross nearest-neighbor distance and torus correction. It reduces the liberality but achieves slightly lower power than the usual cross K-function. Therefore we recommend it, when the point patterns are clustered, where the cross K-function achieves liberality.

Spatial Dependency of Urban Sprawl and the Underlying Road Network Structure

The spatial correlation between urban sprawl and the underlying road network has long been recognized in urban studies. Accessibility to road networks is often considered an approximation for the measurement of human mobility, which is a key factor in determining potential urban sprawl in the future. Despite the close relationship between urban development and road networks, the spatial dependency of these two spatial layers has never been systematically evaluated. This study conducted a comprehensive investigation on the spatial dependency between these two spatial layers using an urban expansion data set between 2000 and 2010 of East Asian regions and the road network data from OpenStreetMap. Four Chinese cities, namely Beijing, Shanghai, Chengdu, and Shenzhen, were selected to conduct the analysis. The spatial correlations between the urban sprawl and road networks were first quantitatively analyzed using Ripley’s cross-K function. Highly significant spatial correlation has been observed in all four tested cities. A Bayesian network model was also developed to verify the predictability of urban sprawl using the spatial and structural features extracted from the existing road networks as well as the spatial pattern of the past built-up areas. The results show an affirmative answer to the predictability of urban sprawl by achieving an overall accuracy of 79% in classifying urban sprawl and undeveloped areas. Finally, the hidden dependencies among the urban sprawl and the extracted spatial features were interpreted and analyzed based on the Bayesian network structure learned from the data.

Flow Cross K-function: a bivariate flow analytical method

ABSTRACTSpatial flow data represent meaningful interaction activities between pairs of corresponding locations, such as daily commuting, animal migration, and merchandise shipping. Despite recent advances in flow data analytics, there is a lack of literature on detecting bivariate or multivariate spatial flow patterns. In this paper we introduce a new spatial statistical method called Flow Cross K-function, which combines the Cross K-function that detects marked point patterns and the Flow K-function that detects univariate flow clustering patterns. Flow Cross K-function specifically assesses spatial dependence of two types of flow events, in other words, whether one type of flows is spatially associated with the other, and if so, whether this is according to a clustering or dispersion trend. Both a global version and a local version of Flow Cross K-function are developed. The former measures the overall bivariate flow patterns in the study area, while the latter can identify anomalies at local scales that may not follow the global trend. We test our method with carefully designed synthetic data that simulate the extreme situations. We exemplify the usefulness of this method with an empirical study that examines the distributions of taxi trip flows in New York City.

A graph-based approach for detecting spatial cross-outliers from two types of spatial point events

Spatial point events are a series of point entities with location information (e.g., longitude and latitude) that describe geographical events, such as crime events. The detection of outliers from spatial point events is very helpful in uncovering unusual geographical phenomena. Existing outlier detection methods mainly focus on single type of events. In practice, it is common that two (or more) types of geographical events can co-occur within a certain spatial region. In this case, the concept of spatial cross-outliers is defined that considers different types of events simultaneously. This study presents an adaptive graph-based approach to fully and accurately detect spatial cross-outliers from two types of spatial point events, which are categorized into target and reference points. First, the cross K-function is utilized to determine whether the reference points are positively dependent on target points or not. On this basis, the spatial cross-neighbourhood relationships between target and reference points are constructed by a two-level edge length constrained Delaunay triangulation and used to quantify the positive dependency degree of reference points on each target point. By considering the spatial distances and local differences of positive dependency degree with respect to target points, the multilevel constrained Delaunay triangulation is further employed to separate spatial cross-outliers. Experiments using both simulated and real-life datasets illustrate that the proposed method can detect spatial cross-outliers in the form of both individual points and collective points with high accuracy and efficiency. Moreover, there is no need to input any parameters.

Network-constrained spatio-temporal clustering analysis of traffic collisions in Jianghan District of Wuhan, China.

The analysis of traffic collisions is essential for urban safety and the sustainable development of the urban environment. Reducing the road traffic injuries and the financial losses caused by collisions is the most important goal of traffic management. In addition, traffic collisions are a major cause of traffic congestion, which is a serious issue that affects everyone in the society. Therefore, traffic collision analysis is essential for all parties, including drivers, pedestrians, and traffic officers, to understand the road risks at a finer spatio-temporal scale. However, traffic collisions in the urban context are dynamic and complex. Thus, it is important to detect how the collision hotspots evolve over time through spatio-temporal clustering analysis. In addition, traffic collisions are not isolated events in space. The characteristics of the traffic collisions and their surrounding locations also present an influence of the clusters. This work tries to explore the spatio-temporal clustering patterns of traffic collisions by combining a set of network-constrained methods. These methods were tested using the traffic collision data in Jianghan District of Wuhan, China. The results demonstrated that these methods offer different perspectives of the spatio-temporal clustering patterns. The weighted network kernel density estimation provides an intuitive way to incorporate attribute information. The network cross K-function shows that there are varying clustering tendencies between traffic collisions and different types of POIs. The proposed network differential Local Moran’s I and network local indicators of mobility association provide straightforward and quantitative measures of the hotspot changes. This case study shows that these methods could help researchers, practitioners, and policy-makers to better understand the spatio-temporal clustering patterns of traffic collisions.

On the location of reported and unreported cycling accidents: A spatial network analysis for Brussels

This paper aims to compare the spatial distributions of road accidents involving a cyclist that are officially reported to the police with those not reported (user-sourced dataset). We show that reported and unreported cycling accidents have similar spatial patterns and exhibit similar locational tendencies with respect to specific infrastructures and facilities. We illustrate the importance of defining the study area in the interpretation of the (cross) K-function results and show that cycling accidents are more likely to be unreported in areas where a small speed difference between slow and fast modes is imposed (traffic-calming areas). Because safety measures influence both accident rate and reporting rate, evaluation of their effect on cycling accidents requires careful spatial analysis.

Discovering non-compliant window co-occurrence patterns

Given a set of trajectories annotated with measurements of physical variables, the problem of Non-compliant Window Co-occurrence (NWC) pattern discovery aims to determine temporal signatures in the explanatory variables which are highly associated with windows of undesirable behavior in a target variable. NWC discovery is important for societal applications such as eco-friendly transportation (e.g. identifying engine signatures leading to high greenhouse gas emissions). Challenges of designing a scalable algorithm for NWC discovery include the non-monotonicity of popular spatio-temporal statistical interest measures of association such as the cross-K function which renders the anti-monotone pruning based algorithms (e.g. Apriori) inapplicable for such interest measures. In our preliminary work, we proposed two upper bounds for the cross-K function and a top-down multi-parent tracking approach that uses these bounds for filtering out uninteresting candidate patterns and then applies a minimum support (i.e. frequency) threshold as a post-processing step to filter out chance patterns. In this paper, we propose a novel bi-directional pruning approach (BDNMiner) that combines top-down pruning based on the cross-K function threshold with bottom-up pruning based on the minimum support threshold to efficiently mine NWC patterns. Case studies with real world engine data demonstrates the ability of the proposed approach to discover patterns which are interesting to engine scientists. Experimental evaluation on real-world data show that the proposed approach yields substantial computational savings compared to prior work.

K-shuff: A Novel Algorithm for Characterizing Structural and Compositional Diversity in Gene Libraries.

K-shuff is a new algorithm for comparing the similarity of gene sequence libraries, providing measures of the structural and compositional diversity as well as the significance of the differences between these measures. Inspired by Ripley’s K-function for spatial point pattern analysis, the Intra K-function or IKF measures the structural diversity, including both the richness and overall similarity of the sequences, within a library. The Cross K-function or CKF measures the compositional diversity between gene libraries, reflecting both the number of OTUs shared as well as the overall similarity in OTUs. A Monte Carlo testing procedure then enables statistical evaluation of both the structural and compositional diversity between gene libraries. For 16S rRNA gene libraries from complex bacterial communities such as those found in seawater, salt marsh sediments, and soils, K-shuff yields reproducible estimates of structural and compositional diversity with libraries greater than 50 sequences. Similarly, for pyrosequencing libraries generated from a glacial retreat chronosequence and Illumina® libraries generated from US homes, K-shuff required >300 and 100 sequences per sample, respectively. Power analyses demonstrated that K-shuff is sensitive to small differences in Sanger or Illumina® libraries. This extra sensitivity of K-shuff enabled examination of compositional differences at much deeper taxonomic levels, such as within abundant OTUs. This is especially useful when comparing communities that are compositionally very similar but functionally different. K-shuff will therefore prove beneficial for conventional microbiome analysis as well as specific hypothesis testing.

Spatial obfuscation methods for privacy protection of household-level data

The topic of geoprivacy is increasingly relevant as larger quantities of personal location data are collected and shared. The results of scientific inquiries are often spatially suppressed to protect confidentiality, limiting possible benefits of public distribution. Obfuscation techniques for point data hold the potential to enable the public release of more accurate location data without compromising personal identities. This paper examines the application of four spatial obfuscation methods for household survey data. Household privacy is evaluated by a nearest neighbor analysis, and spatial distribution is measured by a cross-k function and cluster analysis. A new obfuscation technique, Voronoi masking, is demonstrated to be distinctively equipped to balance between protecting both household privacy and spatial distribution.

Spatial pattern of landslides in Swiss Rhone Valley

The present study analyses the spatial pattern of quaternary gravitational slope deformations (GSD) and historical/present-day instabilities (HPI) inventoried in the Swiss Rhone Valley. The main objective is to test if these events are clustered (spatial attraction) or randomly distributed (spatial independency). Moreover, analogies with the cluster behaviour of earthquakes inventoried in the same area were examined. The Ripley’s K-function was applied to measure and test for randomness. This indicator allows describing the spatial pattern of a point process at increasing distance values. To account for the non-constant intensity of the geological phenomena, a modification of the K-function for inhomogeneous point processes was adopted. The specific goal is to explore the spatial attraction (i.e. cluster behaviour) among landslide events and between gravitational slope deformations and earthquakes. To discover if the two classes of instabilities (GSD and HPI) are spatially independently distributed, the cross K-function was computed. The results show that all the geological events under study are spatially clustered at a well-defined distance range. GSD and HPI show a similar pattern distribution with clusters in the range 0.75–9 km. The cross K-function reveals an attraction between the two classes of instabilities in the range 0–4 km confirming that HPI are more prone to occur within large-scale slope deformations. The K-function computed for GSD and earthquakes indicates that both present a cluster tendency in the range 0–10 km, suggesting that earthquakes could represent a potential predisposing factor which could influence the GSD distribution.

Separate and unequal: The influence of neighborhood and school characteristics on spatial proximity between fast food and schools

ObjectiveSocial science and health literature have identified residential segregation as a critical factor in exposure to health-related resources, including food environments. Differential spatial patterning of food environments surrounding schools has significant import for youth. We examined whether fast food restaurants clustered around schools in New York City, and whether any observed clustering varied as a function of school type, school racial demographics, and area racial and socioeconomic demographics. MethodWe geocoded fast food locations from 2006 (n=817) and schools from 2004–2005 (n=2096; public and private, elementary and secondary) in the five boroughs of New York City. A point process model (inhomogeneous cross-K function) examined spatial clustering. ResultsA minimum of 25% of schools had a fast food restaurant within 400m. High schools had higher fast food clustering than elementary schools. Public elementary and high schools with large proportions of Black students or in block groups with large proportions of Black residents had higher clustering than White counterparts. Finally, public high schools had higher clustering than private counterparts, with 1.25 to 2 times as many restaurants than expected by chance. ConclusionThe results suggest that the geography of opportunity as it relates to school food environments is unequal in New York City.