Cross-mapping Method Research Articles

Contributions of Soil Moisture and Vegetation on Surface-Air Temperature Difference during the Rapid Warming Period

The difference (DIF) between land surface temperature (Ts) and near surface air temperature (Ta) is the key indicator of the energy budget of the land surface, which has a more complex process than the individual Ts or Ta. However, the spatiotemporal variations and influencing factors of DIF remain incomplete. The contribution of vegetation and soil moisture (SM) as key driving factors to DIF is not yet clear. Here, we analyzed the spatiotemporal variation patterns of DIF in China from 2011 to 2023 using in situ Ts and Ta data. A convergent cross-mapping method was employed to explore the causal relationship between SM, NDVI and DIF, and subsequently calculated the contribution of NDVI and SM variations to DIF under different climatic backgrounds. The results indicate that during the study period, DIF values were all above 0 °C and showed a significant increasing trend with a national mean slope of 0.02 °C/a. In general, vegetation and SM have a driving effect on DIF, with vegetation contributing more to DIF (0.11) than SM (0.08) under different surface properties. The background values of SM and temperature have a significant effect on the spatial and temporal distribution of DIF, as well as the correlation of vegetation and soil moisture to DIF. The study outcomes contribute to a better understanding of the coupling relationship between the land surface and atmosphere, which are also crucial for addressing climate change and ecological environmental management.

Detecting causal relationships between fine particles and ozone based on observations in four typical cities of China

As the concentration of fine particles (PM2.5) is declining, ozone (O3) concentration has been increasing in China in recent years. To collaboratively control PM2.5 and O3, it is critical to understand the relationship between the two and identify major controlling factors. We use a convergent cross-mapping method to detect the causal relationship between daily PM2.5 and maximum daily 8 h average (MDA8) O3 concentrations in Beijing, Taizhou, Shenzhen and Chengdu, China, in the four seasons in 2015–2021. In addition, we also examined causal effects of atmospheric oxidation capacity, precursors and meteorological elements on PM2.5 and MDA8 O3 in the four cities. PM2.5 and MDA8 O3 are strongly positively correlated and show bidirectional causal relationships during the Beijing and Taizhou summer and in the four seasons in Shenzhen, due mainly to the strong photochemical reactions in the daytime. During the Beijing winter, PM2.5 and MDA8 O3 show bidirectional causal relationships, but the two are significantly negatively correlated, driven by NO2 and relative humidity. Weak bidirectional, unidirectional and no causal effects between PM2.5 and MDA8 O3 are detected in other seasons in the four cities. In these seasons and cities, the top three causal factors of PM2.5 differ from those of MDA8 O3. Season-, city- and pollutant-specific control measures of PM2.5 and MDA8 O3 are required.

Nursing diagnoses in patients with COVID-19 admitted to the intensive care unit: CROSS-MAPPING

ObjectiveTo identify and analyze the nursing diagnoses listed in the medical records of COVID-19 patients admitted to an intensive care unit using Taxonomy II of NANDA-I. Background: COVID-19 is a complex disease with heterogeneous behaviors, and the role of intensive care nurses in accurately identifying related signs and symptoms has become even more critical during the pandemic. Nurses rely on classification systems or taxonomies to standardize concepts and language in practice. Method: This quantitative study employed a descriptive and individual approach, utilizing the cross-mapping method. Data were collected from 57 medical records of critical care patients in a hospital in northeastern Brazil between July 2020 and March 2021. Three researchers analyzed the mapped diagnoses, and agreement was assessed using the Content Validation Index and Fleiss' Kappa. Results: Among the listed nursing diagnoses, 54.28% were found to be standardized, 45.71% had corresponding nursing diagnoses, and 5.71% did not have an equivalent diagnosis in the reference taxonomy used in the study. Due to the possibility of multiple nursing diagnoses in the same patient, the most frequent diagnoses were Risk of pressure injury in adults (66.66%), Risk of falls in adults (64.91%), and Risk of infection (45.61%). Among the 37 diagnoses mapped, the risk diagnoses were the most prevalent and could be prevented if identified early. Conclusions: The study highlights the importance of standardized nursing diagnoses in the ICU for COVID-19 patients and the need for accurate identification and prevention of risk diagnoses to enhance patient care and improve outcomes.

Quantifying interactions in the water-energy-food nexus: data-driven analysis utilizing a causal inference method

Introduction: There is a pressing need for a holistic approach to optimize water-energy-food (WEF) resources management and to address their interlinkages with other resources due to population growth, socio-economic development, and climate change. However, the structural and spatial extent of the WEF system boundaries cause exponential growth in computational complexity, making exploratory data analysis crucial to obtain insight into the system’s characteristics and focus on critical components.Methods: This study conducts a multiscale investigation of the WEF nexus within the Canadian prairie provinces (Alberta, Saskatchewan, and Manitoba), utilizing causal-correlational analysis and the multispatial Convergence Cross Mapping (mCCM) method. Initially, we employed regression analysis to establish equations, along with their coefficients of determination (R2), to identify patterns among pairs of WEF sectors, gross domestic product (GDP), and greenhouse gas (GHG) emissions. Subsequently, we conducted a causal analysis between correlated pairs using the mCCM method to explore the cause-and-effect relationships between sector pairs within the Canadian prairie provinces; both individually and as a single unit over the period 1990-2020.Results and discussion: Results show that energy and water are the most influential sectors on GHG emissions and GDP in the prairies as a whole. Energy has a stronger influence on GHG compared to water and food sectors, while water has the strongest causal influence on the GDP of Alberta, and food and energy do so for Saskatchewan and Manitoba, respectively. The trade-offs for improving WEF nexus security strongly depend on the scale of the system under investigation, highlighting the need for careful deliberations around boundary judgment for decision-making. This study provides a better understanding of the WEF-GDP-GHG nexus in the Canadian prairies and existing interrelationships among the aforementioned sectors, helping to build more efficient WEF nexus models for further simulation and scenario analysis.

CAT Bridge: an efficient toolkit for gene-metabolite association mining from multiomics data.

With advancements in sequencing and mass spectrometry technologies, multiomics data can now be easily acquired for understanding complex biological systems. Nevertheless, substantial challenges remain in determining the association between gene-metabolite pairs due to the nonlinear and multifactorial interactions within cellular networks. The complexity arises from the interplay of multiple genes and metabolites, often involving feedback loops and time-dependent regulatory mechanisms that are not easily captured by traditional analysis methods. Here, we introduce Compounds And Transcripts Bridge (abbreviated as CAT Bridge, available at https://catbridge.work), a free user-friendly platform for longitudinal multiomics analysis to efficiently identify transcripts associated with metabolites using time-series omics data. To evaluate the association of gene-metabolite pairs, CAT Bridge is a pioneering work benchmarking a set of statistical methods spanning causality estimation and correlation coefficient calculation for multiomics analysis. Additionally, CAT Bridge features an artificial intelligence agent to assist users interpreting the association results. We applied CAT Bridge to experimentally obtained Capsicum chinense (chili pepper) and public human and Escherichia coli time-series transcriptome and metabolome datasets. CAT Bridge successfully identified genes involved in the biosynthesis of capsaicin in C. chinense. Furthermore, case study results showed that the convergent cross-mapping method outperforms traditional approaches in longitudinal multiomics analyses. CAT Bridge simplifies access to various established methods for longitudinal multiomics analysis and enables researchers to swiftly identify associated gene-metabolite pairs for further validation.

Causal mediation of urban temperature by geopotential height in U.S. cities

Excessive warming is the source of many environmental challenges in urban areas. Finding causal interactions between urban ambient temperature and other meteorological variables will greatly facilitate our understanding of the underlying mechanisms of urban heat. In this study, we use the data of 2-m air temperature and 500 hPa geopotential height (GPH) in 520 cities in the contiguous United States (CONUS), from 2016 to 2022, to detect their local and nonlocal causal interactions based on the convergent cross-mapping method. For local (within the same city) interactions between temperature and GPH, there are hubs of strong causal interactions in the northern Appalachian Mountain and inland southwestern CONUS, whereas the leeward side of the southern Rocky Mountains exhibit low causation due to the baroclinic in this area. The nonlocal causal networks exhibit potential long-range connections (teleconnections), largely attributable to the influence of the upstream and downstream westerly circulations on local atmospheric variables. This study can be informative to stakeholders in design sustainable countermeasures to mitigate excessive heat in urban areas.

An exploration of meteorological effects on PM2.5 air quality in several provinces and cities in Vietnam

Linking meteorology and air pollutants is a key challenge. The study investigated meteorological effects on PM2.5 concentration using the advanced convergent cross mapping method, utilizing hourly PM2.5 concentration and six meteorological factors across eight provinces and cities in Vietnam. Results demonstrated that temperature (ρ = 0.30) and radiation (ρ = 0.30) produced the highest effects, followed by humidity (ρ = 0.28) and wind speed (ρ = 0.24), while pressure (ρ = 0.22) and wind direction (ρ = 0.17) produced the weakest effects on PM2.5 concentration. Comparing the ρ values showed that temperature, wind speed, and wind direction had greater impacts on PM2.5 concentration during the dry season whereas radiation had a more influence during the wet season; Southern stations experienced larger meteorological effects. Temperature, humidity, pressure, and wind direction had both positive and negative influences on PM2.5 concentration, while radiation and wind speed mostly had negative influences. During PM2.5 pollution episodes, there was more contribution of meteorological effects on PM2.5 concentration indicated by ρ values. At contaminated levels, humidity (ρ = 0.45) was the most dominant factor affecting PM2.5 concentration, followed by temperature (ρ = 0.41) and radiation (ρ = 0.40). Pollution episodes were pointed out to be more prevalent under higher humidity, higher pressure, lower temperature, lower radiation, and lower wind speed. The ρ calculation also revealed that lower temperature, lower radiation, and higher humidity greatly accelerated each other under pollution episodes, further enhancing PM2.5 concentration. The findings contributed to the literature on meteorology and air pollution interaction.

Feasibility of the Omaha system for the care of children with dilated cardiomyopathy.

To explore the feasibility of Omaha system theory in the care of children with dilated cardiomyopathy (DCM), which may provide a practical basis for the continuous nursing of DCM children. A total of 1,392 records describing symptoms, signs, and nursing interventions were extracted from the medical records of 76 children suffered from DCM. Content analysis method was used to find out existent nursing problems, make precise nursing plans, and take corresponding nursing measurements according to the medical records of DCM children. Cross-mapping method was utilized to compare the conceptual consistency of the medical records and Omaha system (problem classification and intervention subsystems). Of the total 1,392 records, 1,094 (78.59%) were complete consistency, while 245 (17.60%) were partial consistency, and 53 (3.81%) were inconsistency with the Omaha system concepts. The concept matching degree of medical records and Omaha system was approximately 96.19%. The Omaha system may be an effective nursing language for Chinese DCM children, which may be useful to guide nurses in the care of DCM. Further well-design studies need to fully evaluate the feasibility and effectiveness of the Omaha system in nursing children with DCM.

Observational evidence for detrimental impact of inhaled ozone on human respiratory system

The detrimental influence of inhaled ozone on human respiratory system is ambiguous due to the complexity of dose response relationship between ozone and human respiratory system. This study collects inhaled ozone concentration and respiratory disease data from Shenzhen City to reveal the impact of ozone on respiratory diseases using the Generalized Additive Models (GAM) and Convergent Cross Mapping (CCM) method at the 95% confidence level. The result of GAM exhibits a partially significant lag effect on acute respiratory diseases in cumulative mode. Since the traditional correlation analysis is incapable of capturing causality, the CCM method is applied to examine whether the inhaled ozone affects human respiratory system. The results demonstrate that the inhaled ozone has a significant causative impact on hospitalization rates of both upper and lower respiratory diseases. Furthermore, the harmful causative effects of ozone to the human health are varied with gender and age. Females are more susceptible to inhaled ozone than males, probably because of the estrogen levels and the differential regulation of lung immune response. Adults are more sensitive to ozone exposure than children, potentially due to the fact that children need longer time to react to ozone stress than adults, and the elderly are more tolerant than adults and children, which may be related to pulmonary hypofunction of the elderly while has little correlation with ozone exposure.

Collective dynamics analysis based on the multiplex network method to unravel the backbone of fluctuations in groundwater level data

Collective behavior of groundwater level (GWL) in the Tabriz plain, northwest Iran, was modeled in the framework of complex networks. The GWL is considerably influenced by the lack of recharge due to drought in recent years and the increasing water demand of the industrial city of Tabriz. In this order, convergent cross-mapping (CCM) method was utilized to infer the causal relations by adopting a robust statistical approach based on hypothesis testing. Reconstructing structure is a challenge in network-based approaches to capture the dynamical variability of the measurements.This study aims to construct functional connectivity for a better understanding of informational flows among the wells. Multiplex network (MUX) was used as a set of coupled networks through interconnected layers to structure the information obtained from collective dynamics and time-reversal. The proposed procedure was evaluated by performing a systematic analysis of random network (RN) as a well-known model to consider the topological characteristics. The influence of connectivity reconstruction on network topology was also investigated by the generated experiments for different numbers of the dynamical units and lengths of the simulations at each unit. The MUX was constructed from the GWL for monthly observations over 15 years (2001–2017). Afterwards, the time-series was divided into three categories to infer the network connections in different time periods for various sets of the monitoring wells.The analysis indicates that unphysical connections are reduced by increasing the number of the coupling units as a desirable feature for detecting the underlying connectivity. The MUX is employed with the proposed statistical approach to quantitatively unravel the backbone of fluctuations in the GWL whose indirect causal relations form the skeleton. The MUX dynamics efficiently determines the underlying processes and identifies spatio-temporal patterns of the GWL fluctuations in two layers of the constructed networks.

Causality analysis in type 1 diabetes mellitus with application to blood glucose level prediction

Effective control of blood glucose level (BGL) is the key factor in the management of type 1 diabetes mellitus (T1D). BGL prediction is an important tool to help maximise the time BGL is in the target range and thus minimise both acute and chronic diabetes-related complications. To predict future BGL, histories of variables known to affect BGL, such as carbohydrate intake, injected bolus insulin, and physical activity, are utilised. Due to these identified cause and effect relationships, T1D management can be examined via the causality context. In this respect, this work initially investigates these relations and quantifies the causality strengths of each variable with BGL using the convergent cross mapping method (CCM). Then, considering the extended CCM, the causality strengths of each variable for different lags are quantified. After that, the optimal time lag for each variable is determined according to the quantified causality effects. Subsequently, the feasibility of leveraging causality information as prior knowledge for BGL prediction is investigated by proposing two approaches. In the first approach, causality strengths are used as weights for relevant affecting variables. In the second approach, the optimal causal lags and the corresponding causality strengths are considered the shifts and weights for the variables, respectively. Overall, the evaluation criteria and statistical analysis used for comparing results show the effectiveness of using causality analysis in T1D management.

SEXUALIDADE AFETADA DE PESSOAS IDOSAS E AS LIGAÇÕES NANDA-I/NOC/NIC: MAPEAMENTO CRUZADO

ABSTRACT Objective: to map Nursing diagnoses, outcomes and interventions for factors that affect aged people's sexuality. Method: a descriptive study that used the cross-mapping method to establish the links between the NANDA-International Nursing diagnoses, outcomes and interventions, the Nursing Outcomes Classification and the Nursing Interventions Classification, for the factors that affect sexuality identified in aged residents from a public gerontological center in the city of Aguascalientes, Mexico. The data were collected between April and September 2021. A phenomenological study revealed the elements that affect sexuality; subsequently, the Nursing diagnoses were mapped and links with Nursing outcomes and interventions were established, based on specialists' consensus. Results: a total of 11 Nursing diagnoses were mapped, more prevalent among the Perception/Cognition, Self-perception and Health Promotion domains from the NANDA-International taxonomy; as well as 10 different Nursing outcomes from the Nursing Outcomes Classification belonging to the Functional Health, Physiological Health, Psychosocial Health and Health Knowledge and Behavior domains; and 11 Nursing interventions, in the Basic Physiological and Behavioral domains from the Nursing Interventions Classification. Conclusion: Nursing diagnoses, outcomes and interventions were identified, addressing the recognized factors that affect aged people's sexuality.

Quantifying the Influences of Driving Factors on Land Surface Temperature during 2003–2018 in China Using Convergent Cross Mapping Method

The relationship between land surface temperature (LST) and environmental factors is complex and nonlinear. To determine these relationships for China, this study analyzed the driving effects of air temperature, vegetation index, soil moisture, net surface radiation, precipitation, aerosols, evapotranspiration, and water vapor on LST based on remote-sensing and reanalysis data from 2003–2018, using a convergent cross-mapping method. During the study period, air temperature and net surface radiation were the dominant drivers of LST with a cross-mapping skill above 0.9. Vegetation index and evapotranspiration were the secondary drivers of LST with a cross-mapping skill that was higher than 0.5. Except for air temperature and net surface radiation, the direction and strength of the effects of the driving factors on LST were related to the climate type. The effects of air temperature and net radiation on LST diminished from north to south, indicating that LST was more sensitive to air temperature and net radiation in energy-limited regions. However, the effects of vegetation index and evapotranspiration on LST varied significantly across climate zones; that is, positive effects were mostly in non-monsoonal zones and negative effects were primarily in monsoonal zones. Our results quantified the driving role of environmental factors on LST and provided a comprehensive understanding of LST dynamics.

Identifying changes in China's Bohai and Yellow Sea fisheries resources using a causality-based indicator framework, convergent cross-mapping, and structural equation modeling

There is growing evidence that the number of fish stocks that are being harvested at biologically unsustainable levels has increased due to a number of threats. In order to identify the key threats to fisheries resources in the Bohai Sea and Yellow Sea, a causality-based indicator system of fish stock trends and main influencing factors was developed in this study. The causal relationship and influence degree of the driving factors were determined by using the method of convergent cross-mapping, and the structural equation model of fisheries resources change under the influence of multiple factors was established. The results showed that the path coefficients of anthropogenic factors were 1.25 and 1.00 in the Bohai Sea and Yellow Sea, respectively, which were obvious higher than that of environmental factors (0.88 and 0.01), so the influence of anthropogenic factors on fisheries resources was greater than that of environmental factors. There are similarities and differences among the key factors affecting the decline of fisheries resources in the two sea areas. For anthropogenic factors, marine catch and mariculture are the main driving forces in the Bohai Sea and Yellow Sea, followed by the size of marine protected areas. For environmental factors, COD and reactive phosphorus concentration affect the fisheries in the Bohai Sea and Yellow Sea, respectively. Furthermore, some pertinent suggestions were given in this study according to the characteristics of fisheries resources in the Bohai Sea and Yellow Sea. These findings will help fisheries managers in China protect fisheries resources and the marine environment more effectively, and provide a research foundation to support the sustainable development of China's fisheries in the context of resources decline and environmental degradation.

Causality analysis and prediction of blast furnace state based on convergence cross mapping

ABSTRACT Blast furnace (BF) ironmaking system is a complex industrial system so this paper proposes a BF state causality analysis method based on the use of convergent cross-mapping method (CCM). This method can accurately describe the causal relationships between states at different locations in the BF system. It can also be used as a feature selection method for prediction models. After obtaining accurate causal characteristics of the BF state covariates, the BF system process theory is used for validation. The causal characteristics are used as input variables to the extreme gradient boosting model (XGboost) for predicting BF state parameters. After testing with industrial data, the model predicted an absolute error control within 2% with an accuracy of over 88%. The CCM approach mentioned in this paper is more suitable for state causal impact analysis and predictive model feature selection for BF systems.

A complex network approach for the model of vehicle emission propagation and intelligently mine the interaction rules

With the increasing number of motor vehicles, exhaust emission has become a major source of urban pollution. Most studies are limited to the prediction of pollutant concentration, which cannot clearly indicate the change of pollution emissions and regional relationship. In this paper, we propose an emission propagation model of vehicle source pollution based on complex network in order to intelligently mine the interaction and propagation rules hidden behind dynamic spatiotemporal data. First, aiming at the problems of low resolution and insufficient data volume of vehicle emission data, a high-resolution pollution emission data is generated based on the COPERT (Computer Program to Calculate Emissions from Road Transport). For study the influence of causality between regions, a propagation model is designed based on the convergent cross mapping method to transform the emission time series into a complex network. In addition, we propose a novel key node mining algorithm using hybrid local and global information to identify areas of heavy pollution. Experimental results on real datasets demonstrate that the spread of pollution follows certain rules and is also affected by regional influences. Moreover, the proposed algorithm is superior to the state-of-the-art methods.

Cross-mapping medical records to NANDA-I to identify nursing diagnoses in a vulnerable population.

To assess the association between vulnerable populations and nursing care needs, using NANDA-I diagnostics, in the population of the Canary Islands, Spain. Nursing social epidemiology study. Cross Mapping of Medical Records to NANDA-I to Identify Nursing Diagnoses in a Population usinga medical, epidemiological follow-up study of a cohort of 7,190 people. The level of vulnerability of the participants was assigned, among those who were also assigned nursing diagnoses, using the "ICE index" to calculate the expected associations. The most prevalent nursing diagnosis in our sample was Sedentary lifestyle (60.5%), followed by Ineffective health self-management (33.8%) and Risk-prone health behaviour (28.7%). Significant differences were found by sex, age group and social class, with the nursing diagnoses included in the study being more prevalent among the most socio-economically disadvantaged social class. The cross-mapping method is useful to generate diagnostic information in terms of care needs, using the NANDA-I classification. The expected associations between high social vulnerability and care needs have been verified in a comprehensive and representative sample of the Canarian population (Spain). From an epidemiological perspective, identifying nursing diagnoses at the population level allows us to find the most prevalent needs in the different community groups and to focus appropriate nursing interventions for their implementation and impact assessment.

Migration and diffusion characteristics of air pollutants and meteorological influences in Northwest China: a case study of four mining areas.

In the process of exploiting mineral resources, dust enters the environment through air suspended particles and surface runoff, which has a serious impact on the atmospheric environment and human health. From all-year and seasonal scenarios, the migration trajectories and cumulative concentration based on the secondary development of Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) in four mining areas (SF, BC, SJZ, and MJT) in Northwest China are studied. The convergent cross mapping (CCM) method is used to study the causal relationship between concentration and meteorological factors. In this process, the problem of missing non-station meteorological data is solved with the help of the inverse distance weighted interpolation method, and the problem in which the convergence requirements of the CCM algorithm cannot meet the requirements is solved with the bootstrap method. The results indicated that the short path has the characteristics of slow movement, short migration path, low altitude(< 1 km), and high contribution rate, while the long path has the opposite characteristics. Furthermore, the results demonstrated that the concentration is centered on the pollution source and diffuses around, with a diffusion radius of 220–270 km, showing a serious pollution center and slight gradient settlement on the edge, but the overall distribution of accumulated concentration is uneven. The results also show that temperature (TEMP and S_TEMP), evaporation, and air pressure are the main meteorological factors affecting the all-year concentration. The concentration and meteorological factors in the four mining areas also show significant seasonal characteristics, and the correlation in spring, summer, and autumn is stronger than that in winter. This study not only provides a reference for the green and sustainable exploitation of mineral resources but also provides theoretical support for the joint prevention and control of transboundary pollution.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11356-022-19706-w.

The Roles of Fractionated Potentials in Non-Macroreentrant Atrial Tachycardias Following Atrial Fibrillation Ablation: Recognition Beyond Three-Dimensional Mapping.

IntroductionNon-macroreentrant atrial tachycardia (nAT) following atrial fibrillation (AF) ablation is being increasingly reported. Many issues remain to be elucidated. We aimed to characterize the fractionated potentials (FPs) in nAT and introduce a new method of cross-mapping for clarifying their roles.Methods and ResultsForty-four nATs in 37 patients were enrolled and classified into focal AT (FAT, 12), microreentrant AT (MAT, 14), and small-loop-reentrant AT (SAT, 18) groups, according to activation pattern. FP was found on all targets except in nine FATs. The ratio of FP duration to AT cycle length (TCL) was different among groups (28 ± 7% in FAT, 53 ± 11% in MAT, and 42 ± 14% in SAT, p < 0.05), and ablation duration were longer in SATs (313 ± 298 vs. 111 ± 125 s, p < 0.05). The ratio of mappable cycle length to TCL was lower in the FAT group (63 ± 22% vs. 90 ± 9% and 89 ± 8%, p < 0.05). When cross-mapping was employed, trans-potential time differences in both longitudinal and transverse direction were longer around the culprit FP for MAT (p < 0.01). After Receiver Operating Characteristic curve analysis, it is best to adopt the sum of time difference ratios in both directions ≥60% as a cut-off value for discrimination of the FPs responsible for MAT with a sensitivity of 92% and specificity of 87%.ConclusionsFP could be found on target in most nATs following a previous AF ablation. The ratio of FP duration to TCL may help for differentiation. A simple method of cross-mapping could be employed to clarify the roles of FPs.

Detecting delay propagation in regional air transport systems using convergent cross mapping and complex network theory

It has been widely recognized that delay propagation is a widespread phenomenon in air transport systems. Regional air transport systems are vulnerable to severe systemic delay propagation because of connected resources and shared airspace. This study presents a two-stage analytical framework to detect delay propagation in regional air transport systems, which is critical to support industrial applications in air transport operations. In the first stage, we propose a delay causality without the strong and independent causality (SIC) assumption to represent the delay propagation effect. A convergent cross mapping method is employed to obtain the delay causality. In the second stage, we build a delay causality graph based on the none SIC assumption (DCG-non-SIC). A complex network analysis of DCG-non-SIC is presented to enhance the understanding of delay propagation patterns. This study carries out a real-world case study and provides some interesting results. Robustness checks are conducted, which verifies that the results derived in the analytical framework are solid. The results show that there is extensive delay causality between airport pairs, and a transitive trait of delay causality is observed in regional air transport systems. In addition, the importance of airports in delay propagation is not exactly in line with the hub class or the airport size.