Joint Probability Research Articles

Bivariate Lomax Distribution Based on Clayton Copula: Estimation and Prediction

Lomax distribution has been studied by many statisticians due to its important role in reliability modeling and lifetime testing. The bivariate Lomax distribution is an important lifetime distribution in survival analysis. In this article, a bivariate Lomax distribution is constructed based on Clayton copula. The joint probability density function and the joint cumulative distribution function are derived in closed forms. Some properties of this bivariate distribution are discussed. The maximum likelihood and Bayes estimators for the unknown parameters are derived. Also, the maximum likelihood and Bayesian two-sample prediction for the future observations are obtained. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, one real data set under the proposed distribution is considered to illustrate its flexibility and applicability for real-life applications.

Drought and wetness events encounter and cascade effect in the Yangtze River and Yellow River Basin

Under the background of global change, the multivariate attributes, multi-temporal and multi-watershed regional characteristics of extreme drought and flood disasters are significant. It is very important to identify the drought and wetness encounter law and spatial cascade effect in the source region-upper-middle-lower reaches of the basin. In this paper, the Yangtze River and Yellow River basins are taken as the research objects. Based on the standardized precipitation index (SPI) characterizing meteorological drought and wetness and the standardized runoff index (SRI) characterizing hydrological drought and wetness, the evolution law of extreme drought and flood events in the source region-upper-middle-lower reaches of the two basins is analyzed. On this basis, the correlation analysis and transfer function analysis are used to explore the response relationship and lag effect between the two in different partitions. A two-dimensional joint distribution model is constructed by Copula function to quantitatively analyze the joint probability of drought and wetness encounters of 9 combined events, and to deeply analyze the impact of different drought and wetness encounter scenarios. The results show that: from 1957 to 2020, the two basins showed a trend from drought to wet. The SPI-12 in the Yellow River Basin ranged from-1.57 to 1.32, and that in the Yangtze River Basin ranged from-1.24 to 1.11. The severity of drought and wetness in the Yellow River Basin was higher than that in the Yangtze River Basin; The correlation coefficients between SPI and SRI in the source-upper-middle-lower reaches of the Yellow River (Yangtze River) were 0.78 (0.76), 0.23 (0.73), 0.44 (0.55) and 0.23 (0.63), respectively. The correlation degree of meteorological-hydrological drought and wetness in the Yangtze River Basin was significantly higher than that in the Yellow River Basin. The average probability of synchronous combination events of drought and wetness in the two basins is greater than 51.43 %. The probability of drought in the Yellow River Basin is greater than that of flood, while the Yangtze River Basin is the opposite. In the same drought and wetness scenario, an average of 54.1% of the event pairs were aggravated by disasters, and more than 52 % of the events in the wetness-drought scenario had obvious drought mitigation effects. The research results can provide important support for improving the early warning and risk management of river basin disasters.

A PINN-DeepONet framework for extracting turbulent combustion closure from multiscalar measurements

In this study, we develop a novel framework to extract turbulent combustion closure, including closure for species chemical source terms, from multiscalar and velocity measurements in turbulent flames. The technique is based on a physics-informed neural network (PINN) that combines models for velocity and scalar measurements and a deep operator network (DeepONet) to accommodate spatial measurements and experimental parameters as separate input streams. An additional key innovation is the estimate of the unconditional means of the species’ chemical source terms as additional “observations” to constrain the prediction of these rates. This estimate is based on a convolution of the means of species reaction rates conditioned on principal components of the multiscalar data and the joint probability density functions of these principal components. The PINN-DeepONet method is implemented on the so-called Sydney flames, where training is carried out on 3 flames and validated on 4 flames. The results show that, despite the limited samples of experimental parameters, including the inlet flow and the fuel jet recess length within the air flow, the PINN-DeepONet approach can construct velocity and scalar fields along with important closure terms for turbulent transport and reaction rates.

Estimation of complete mutual information exploiting nonlinear magnitude-phase dependence: Application to spatial FNC for complex-valued fMRI data

BackgroundReal-valued mutual information (MI) has been used in spatial functional network connectivity (FNC) to measure high-order and nonlinear dependence between spatial maps extracted from magnitude-only functional magnetic resonance imaging (fMRI). However, real-valued MI cannot fully capture the group differences in spatial FNC from complex-valued fMRI data with magnitude and phase dependence. MethodsWe propose a complete complex-valued MI method according to the chain rule of MI. We fully exploit the dependence among magnitudes and phases of two complex-valued signals using second and fourth-order joint entropies, and propose to use a Gaussian copula transformation with a lower bound property to avoid inaccurate estimation of joint probability density function when computing the joint entropies. ResultsThe proposed method achieves more accurate MI estimates than the two histogram-based (normal and symbolic approaches) and kernel density estimation methods for simulated signals, and enhances group differences in spatial functional network connectivity for experimental complex-valued fMRI data. Comparison with existing methodsCompared with the simplified complex-valued MI and real-valued MI, the proposed method yields higher MI estimation accuracy, leading to 17.4 % and 145.5 % wider MI ranges, and more significant connectivity differences between healthy controls and schizophrenia patients. A unique connection between executive control network (EC) and right frontal parietal areas, and three additional connections mainly related to EC are detected than the simplified complex-valued MI. ConclusionsWith capability in quantifying MI fully and accurately, the proposed complex-valued MI is promising in providing qualified FNC biomarkers for identifying mental disorders such as schizophrenia.

Updating direct methods II. Reduction of the structural complexity when triplet invariants are estimated via the Patterson map

Direct methods have practically solved the phase problem for small–medium-size molecules but have substantially failed in macromolecular crystallography. They have two main limitations: a strong dependence on structural complexity and the need to work with atomic-resolution data. Many attempts have been made to broaden their field of applicability, for example the use of some a priori information to make the estimate of the triplet invariant phases more effective. Unfortunately none of these new approaches allowed the successful application of direct methods to proteins and nucleic acids. Direct methods are still a niche tool in macromolecular crystallography. In a recent publication [Giacovazzo (2019). Acta Cryst. A75, 142–157] the method of joint probability distributions has been modified to take into account new sources of prior information, one of which is relevant to this article: the Patterson map. In practice, it has been shown that with prior knowledge of the interatomic vectors one is able to modify the classic Cochran reliability parameter for estimating the triplet invariant phases. The article was essentially theoretical in nature, and no attempt was described to test the practical usefulness of the new probabilistic formulas. This work is therefore the first application of the new method. It is shown that the use of the Patterson map as prior information substantially improves the Cochran estimate of triplet phases; the phase error distribution for the new estimates, even if it is related to macromolecular structures, becomes similar to that obtained for medium-size structures. In some ways, it is as if the use of the Patterson information reduces the structural complexity, thus allowing a more general use of direct methods in macromolecular crystallography. Atomic resolution no longer seems to be a necessary ingredient for the applicability of direct methods; tests show that the apparent reduction in structural complexity also occurs in macromolecular structures with experimental data having a resolution of 2.3 Å. A number of test structures have been used to show the potential of the new technique.

Bell inequality violation in relativity theory

A violation of Bell local realism inequalities in Clauser–Horne–Shimony–Holt form has been discovered in a relativistic Gedankenexperiment. This means that there are no definite joint probabilities and this finds a classical explanation in the structure of special relativity. The discovered nonlocality is weaker than Albert Einstein’s quantum ‘spooky action at a distance’, and its presence suggests certain parallels between special relativity and quantum mechanics.

The short-term intermittency evaluation of distributed photovoltaic power

Uncertainty of distributed photovoltaic(PV) power brings great challenges to the safe and stable operation of power system, in which the intermittency problem is more challenging than the fluctuation. This paper focuses on the intermittency problem of distributed PV power, firstly, an intermittency evaluation method based on generalized extreme value(GEV) theory is proposed to solve the problem of the lack of "small-sample big-gap" events. Secondly, focusing on high risk events such as high-frequency and warning mutation events, probabilistic evaluation indexes were established, including T-hour-period mutation intensity and T-hour-period mutation frequency. Finally, a two-dimensional joint probability distribution of intermittency elements is established, and the concepts of return period and return level are introduced into the photovoltaic field to provide data support for the configuration of energy storage capacity and duration, and to provide auxiliary decision-making for the execution time and development cycle of interactive projects. The proposed method provides a solution for intermittency evaluation in small sample status quo with strong data compatibility and engineering replicability.

Satisficing Approach to On-Demand Ride Matching

Online ride-hailing platforms have developed into an integral part of the transportation infrastructure in many countries. The primary task of a ride-hailing platform is to match trip requests to drivers in real time. Although both passengers and drivers prefer a prompt pickup to initiate the trips, it is often difficult to find a nearby driver for every passenger. If the driver is far from the pickup point, the passenger may cancel the trip while the driver is heading toward the pickup point. For the platform to be profitable, the trip cancellation rate must be maintained at a low level. We propose a computationally efficient data-driven approach to ride matching, in which a pickup time target is imposed on each trip request and an optimization problem is formulated to maximize the joint probability of all the pickup times meeting the targets. By adjusting pickup time targets individually, this approach may assign more high-value trip requests to nearby drivers, thus boosting the platform’s revenue while maintaining a low cancellation rate. In numerical experiments, the proposed approach outperforms several ride-matching policies used in practice. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work of D. Rong and X. Sun was supported in part by the National Natural Science Foundation of China [Grant 71971165], the National Key Research and Development Program of China [Grant 2021YFB3301801], the MOE Project of Humanities and Social Science of China [Grant 19YJE630002], and the Soft Science Research Program of Shannxi [Grant 2018KRZ005]. The work of S. He was supported in part by the Singapore Ministry of Education Social Science Research Council [Grant MOE2022-SSRTG-029]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0210 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0210 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Code and Data Repository for Satisficing Approach to On-Demand Ride Matching

Online ride-hailing platforms have developed into an integral part of the transportation infrastructure in many countries. The primary task of a ride-hailing platform is to match trip requests to drivers in real time. Although both passengers and drivers prefer a prompt pickup to initiate their trips, it is often difficult to find a nearby driver for every passenger. If the driver is far from the pickup point, the passenger may cancel the trip while the driver is heading toward the pickup point. In order for the platform to be profitable, the trip cancellation rate must be maintained at a low level. We propose a data-driven, computationally efficient approach to ride matching, in which a pickup time target is imposed on each trip request and an optimization problem is formulated to maximize the joint probability of all the pickup times meeting the targets. By adjusting pickup time targets individually, this approach may assign more high-value trip requests to nearby drivers, thus boosting the platform’s revenue while maintaining a low cancellation rate. In numerical experiments, the proposed approach outperforms several ride-matching policies used in practice.

Performance-based design of environmental parameters for offshore wind turbine foundations

Taking into account the coupling effects of wind, wave, and current on offshore wind turbines (OWTs), a combined approach utilizing non-linear finite element analysis (FEA), back propagation neural network (BPNN), and probabilistic statistical methodology (PSM) is proposed for accurate environmental parameter estimation in OWT foundation design. The structural bearing performances of OWT foundations are precisely predicted through a combination of FEA and BPNN models, and then serve as constraints for probabilistic statistical analysis. Furthermore, for PSM, a robust multivariate joint probability distribution is constructed leveraging copula functions, which not only maximizes marginal information but also effectively captures the intricate dependencies among ocean environmental parameters. Subsequently, the proposed models, along with traditional univariate analysis, are utilized to estimate the return values of diverse load combinations. The results indicate that, for a given return period, the conditional probability model yields lower wave heights and current velocities compared to univariate analysis, while the joint probability model results in lower values for all ocean parameters, making both approaches more suitable for OWT foundation design. This coupled approach presents a more rational and cost-effective solution compared to univariate analysis, potentially resulting in decreased investment costs.

Parameter estimation of grouting pressure and surface subsidence on the reliability of shield tunnel excavation under incomplete probability information

Most of the results obtained from traditional tunnel reliability models are based on conclusions of deterministic parameters, and ignoring the correlation between parameters tends to generate unreliable conclusions for the analysis. This study investigated the influence of grouting pressure and surface subsidence on the reliability of shield tunnel excavation considering the dependency structures between parameters. A probabilistic analysis approach based on copula method is applied to evaluate the bivariate dependency structure. Firstly, 88 sets of measured data are selected from various tunnel projects at home and abroad, and their statistical parameters and marginal distribution functions are determined. Secondly, a bivariate joint probability distribution model of shield grouting excavation is established, and Monte Carlo Simulation is applied to explore the influence of the selection of the copula function on the failure probability of the shield grouting excavation. The results indicate that under incomplete probabilistic information, disregarding the negative correlation between the parameters will underestimate the reliability of shield grouting construction and yield an overly conservative reliability design. Subsequently, varying the magnitude of the parameter limit values to explore the effect on the failure probability will be advantageous for reliability analysis in dynamic construction. Finally, by varying the sample size of the simulation and original measured data, it is found that excessively small simulated and original sample sizes can lead to inaccurate reliability assessment.

Field theory of active chiral hard disks: a first-principles approach to steric interactions

A first-principles approach for active chiral hard disks is presented, that explicitly accounts for steric interactions on the two-body level. We derive an effective one-body equation for the joint probability distribution of positions and angles of the particles. By projecting onto the angular modes, we write a hierarchy for the lowest hydrodynamic modes, i.e. particle density, polarisation, and nematic tensor. Introducing dimensionless variables in the equations, we highlight the assumptions, which—though inherent—are often included implicit in typical closure schemes of the hierarchy. By considering different regimes of the Péclet number, the well-known models in active matter can be obtained through our consideration. Explicitly, we derive an effective diffusive description and by going to higher orders in the closure scheme, we show that this first-principles approach results in the recently introduced Active Model B +, a natural extension of the Model B for active processes. Remarkably, here we find that chirality can change the sign of the phenomenological activity parameters.

Framework for assessing the performance of overhead transmission lines under wind-temperature effects

This paper presents a framework for evaluating the wind-induced resistance of overhead transmission lines (OTLs), aiming to overcome the limitations associated with disregarding temperature effects and relying on a single metric for failure assessment. The proposed framework factors in temperature influence, carefully considers applied loads and structural characteristics, and accurately calculates failure probability based on a specific case study. Meteorological data is initially collected to create a probabilistic model of wind speed and temperature distribution, accounting for correlation. Components and systems are graded based on structural characteristics and damage modes. The neural network surrogate model is trained with finite element computations for load-structural response sample sets. The surrogate model, in conjunction with logistic regression, generates samples to determine fragility. Finally, the total structural failure probability and monthly failure likelihood are computed by integrating the joint probability model and fragility. Analyses highlight temperature's significant impact on conductor-ground line safety, validating the proposed framework's rationale.

Synthesizing PET images from high-field and ultra-high-field MR images using joint diffusion attention model.

Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) stand as pivotal diagnostic tools for brain disorders, offering the potential for mutually enriching disease diagnostic perspectives. However, the costs associated with PET scans and the inherent radioactivity have limited the widespread application of PET. Furthermore, it is noteworthy to highlight the promising potential of high-field and ultra-high-field neuroimaging in cognitive neuroscience research and clinical practice. With the enhancement of MRI resolution, a related question arises: can high-resolution MRI improve the quality of PETimages? This study aims to enhance the quality of synthesized PET images by leveraging the superior resolution capabilities provided by high-field and ultra-high-fieldMRI. From a statistical perspective, the joint probability distribution is considered the most direct and fundamental approach for representing the correlation between PET and MRI. In this study, we proposed a novel model, the joint diffusion attention model, namely, the joint diffusion attention model (JDAM), which primarily focuses on learning information about the joint probability distribution. JDAM consists of two primary processes: the diffusion process and the sampling process. During the diffusion process, PET gradually transforms into a Gaussian noise distribution by adding Gaussian noise, while MRI remains fixed. The central objective of the diffusion process is to learn the gradient of the logarithm of the joint probability distribution between MRI and noise PET. The sampling process operates as a predictor-corrector. The predictor initiates a reverse diffusion process, and the corrector applies Langevindynamics. Experimental results from the publicly available Alzheimer's Disease Neuroimaging Initiative dataset highlight the effectiveness of the proposed model compared to state-of-the-art (SOTA) models such as Pix2pix and CycleGAN. Significantly, synthetic PET images guided by ultra-high-field MRI exhibit marked improvements in signal-to-noise characteristics when contrasted with those generated from high-field MRI data. These results have been endorsed by medical experts, who consider the PET images synthesized through JDAM to possess scientific merit. This endorsement is based on their symmetrical features and precise representation of regions displaying hypometabolism, a hallmark of Alzheimer'sdisease. This study establishes the feasibility of generating PET images from MRI. Synthesis of PET by JDAM significantly enhances image quality compared to SOTAmodels.

Comprehensive evaluation of extreme hydrometeorological events coincidence and their interrelationships in the Hanjiang River Basin, China

Extreme hydrometeorological events are often highly destructive and can cause huge damage to the natural environment and social economy. As climate change and human activities intensify, the frequency and intensity of such extreme events continue to increase. This phenomenon is also shown in the Hanjiang River Basin (HRB) in recent decades. In this study, we focus on the coincidence occurrence patterns of extreme hydrometeorological events. First, we used the standardized index method to extract the annual maximum and minimum values of runoff, precipitation, maximum and minimum temperatures from 1961 to 2019 in the control area of the Baihe (BH) hydrological station, with time scales from 1 month to 12 months. Then through the Copula and nested structure Copula functions, the joint occurrence probability of bivariate and multivariate were analyzed. The results show that too high a maximum temperature will inhibit runoff, while an increase in minimum temperature will promote an increase in runoff to a certain extent. Both the maximum and minimum temperatures in the basin shown a significant increasing trend, and the intensity of hydrological drought also shows an increasing trend. An increase in maximum temperature will aggravate hydrological drought, as the combined joint occurrence probability of them is the greatest. Analysis through the nested structure Copula functions show that when extreme hydrometeorological events both occurred at the median of their intervals, their coincidence occurrence probability is the maximum, and when the time scale is eight months, their coincidence occurrence probability is the highest. This study can provide a reference for joint probability analysis of extreme hydrometeorological events.

A novel GNSS and precipitation-based integrated drought characterization framework incorporating both meteorological and hydrological indicators

The Global Navigation Satellite System (GNSS) has become instrumental in developing drought indices, particularly meteorological drought indicators derived from atmospheric precipitable water vapor and hydrological drought indicators based on inverted terrestrial water storage changes. However, these indices traditionally focus on individual aspects of droughts, either meteorological or hydrological droughts, and do not fully capture the integrated nature of drought phenomena. Addressing this gap, this study proposes a novel integrated drought characterization framework using the Gringorten plotting position to derive joint probabilities for GNSS-derived meteorological and hydrological drought indicators. This leads to the creation of a comprehensive multivariate drought severity index (GNSS-MDSI). The analysis across the western United States indicates significant spatial variability in multiyear average precipitation efficiency, ranging from 7.51% to 28.1%. This variability corresponds with marked differences in seasonal terrestrial water storage changes, which oscillate between 25 and 123 mm. Applying this framework in eight states, 9–13 comprehensive drought events from January 2006 to December 2021, with durations spanning from 3 to 54 months, were identified. The GNSS-MDSI not only captured these comprehensive drought periods across various temporal and spatial scales but also aligned closely with drought classifications provided by the US Drought Monitor. These results underscore the utility of this framework in providing a more nuanced and multifaceted perspective on drought conditions, surpassing the capabilities of single-indicator systems. Overall, this study presents an innovative framework for drought monitoring by integrating two GNSS-derived drought indicators, enabling precise and comprehensive delineation of drought characteristics, and offering a geodesy-based solution for integrated global and regional drought monitoring.

Condition numbers for real eigenvalues of real elliptic ensemble: weak non-normality at the edge

Sensitivity of an eigenvalue λ i to the perturbation of matrix elements is controlled by the eigenvalue condition number defined as κi=⟨Li|Li⟩⟨Ri|Ri⟩ , where ⟨Li| and |Ri⟩ are left and right eigenvectors to the eigenvalue λ i . In random matrix theory the squared eigenvalue condition number is also known as the eigenvector self-overlap. In this work we calculate the asymptotics of the joint probability density function of the real eigenvalue and the square of the corresponding eigenvalue condition number for the real elliptic ensemble in the double scaling regime of almost Hermiticity and close to the edge of the spectrum. As a byproduct, we also calculate the one-parameter deformation of the Scorer’s function.

Pollution Characteristics and Multilevel Risk Assessments of Antibiotics in the Urban Rivers of Beijing, China

To comprehensively assess the pollution characteristics and ecological risks of antibiotics in the rivers in Beijing, the concentrations of 35 common antibiotics belonging to four categories were quantified by using solid phase extraction combined with high-performance liquid chromatography-tandem mass spectrometry. The ecological risks of antibiotics were evaluated using the methods of risk quotient (RQ) and joint probability curves (JPCs). The results showed that a total of 33 antibiotics were detected in the surface water of ten rivers in Beijing, and the total concentrations of antibiotics ranged from N.D. to 1 573.57 ng·L-1. Sulfamethoxazole showed the highest concentration (N.D.-160.04 ng·L-1), followed by sulfadiazine (0.09-147.90 ng·L-1) and ofloxacin (0.28-94.72 ng·L-1). There were 16 antibiotics with a detection frequency greater than 50.0 %. The RQ method showed that there were 12 antibiotics with potential ecological risks. Tetracycline, clarithromycin, and trimethoprim showed the highest risks, with RQs of 3.99, 1.86, and 1.01, respectively. The risks of antibiotics at the outlets of wastewater treatment plants were higher than those in mainstream rivers. The PNEC exceedance rates of tetracycline, clarithromycin, and trimethoprim were above 2.3 %. Based on JPCs, the maximum risk product of clarithromycin was 1.66 %, and it showed low risks to 0.3 %-7.0 % of species. The risks of other antibiotics could be ignored. The detection frequency, distribution of concentrations, most sensitive species, and species sensitivity distribution of antibiotics had important impacts on the ecological risk assessment. Using the multilevel ecological risk assessment strategy can effectively avoid inadequate protection and overprotection and is also conducive to the hierarchical and zoning management of antibiotics throughout the region.

Joint modeling of correlated binary outcomes using multivariate logistic regression: contraception and HIV knowledge in Sri Lanka

Reproductive health significantly contributes to the overall well-being and social welfare of women. Within the spectrum of modern and traditional contraceptive methods in use, condoms have been strongly advocated by numerous HIV programs as a primary means of preventing HIV infection in Sri Lanka. Given the intrinsic relationship between contraceptive utilization and HIV awareness, our study aims to concurrently analyze the patterns of contraceptive usage and HIV knowledge, while accounting for their potential correlation. In this study, we introduced the application of the Gumbel type II distribution to effectively capture the interdependence of these joint probabilities, accounting for various covariates. The outcome of simulation studies demonstrated the superior performance of the integrated joint model, in comparison to the separate univariate models. Our findings highlighted several noteworthy risk factors associated with both contraceptive usage and HIV prevention knowledge. These included variables such as residence, level of education, wealth quintile, husband's education level, number of children, engagement with the newspapers, television viewership, and mobile phone usage. The Result indicates a positive association between the adoption of contraception and the awareness of HIV prevention measures, suggesting that individuals who actively embrace contraception are more likely to possess knowledge about preventing HIV transmission.

Mapping morphological cortical networks with joint probability distributions from multiple morphological features

Morphological features sourced from structural magnetic resonance imaging can be used to infer human brain connectivity. Although integrating different morphological features may theoretically be beneficial for obtaining more precise morphological connectivity networks (MCNs), the empirical evidence to support this supposition is scarce. Moreover, the incorporation of different morphological features remains an open question. In this study, we proposed a method to construct cortical MCNs based on multiple morphological features. Specifically, we adopted a multi-dimensional kernel density estimation algorithm to fit regional joint probability distributions (PDs) from different combinations of four morphological features, and estimated inter-regional similarity in the joint PDs via Jensen-Shannon divergence. We evaluated the method by comparing the resultant MCNs with those built based on different single morphological features in terms of topological organization, test-retest reliability, biological plausibility, and behavioral and cognitive relevance. We found that, compared to MCNs built based on different single morphological features, MCNs derived from multiple morphological features displayed less segregated, but more integrated network architecture and different hubs, had higher test-retest reliability, encompassed larger proportions of inter-hemispheric edges and edges between brain regions within the same cytoarchitectonic class, and explained more inter-individual variance in behavior and cognition. These findings were largely reproducible when different brain atlases were used for cortical parcellation. Further analysis of macaque MCNs revealed weak, but significant correlations with axonal connectivity from tract-tracing, independent of the number of morphological features. Altogether, this paper proposes a new method for integrating different morphological features, which will be beneficial for constructing MCNs.