Panpan Zhang

Panpan Zhang

Assistant Professor at the Vanderbilt University School of Medicine

Publications

Arterial Spin Labeling Hemodynamic Indices Relate to Cognitive and Small Vessel Disease Trajectories Over 11 Years

Published in Stroke, 2026

Higher baseline ASL signal variability was associated with worsening white matter lesions and cognitive decline over follow-up. <DOI | PubMed>

Recommended citation: Robb, W. H., Santner, A. M., Zhang, P., Kim, D. S., Jackson, T. B., Shashikumar, N., Pechman, K. R., Vyas, Y., Liu, D., Davis, L. T., Hohman, T. J. and Jefferson, A. L. (2026). "Arterial Spin Labeling Hemodynamic Indices Relate to Cognitive and Small Vessel Disease Trajectories Over 11 Years." Stroke. Advance online publication. https://doi.org/10.1161/STROKEAHA.125.054879. https://doi.org/10.1161/STROKEAHA.125.054879

Lower cardiac output is a risk factor for faster cerebral atrophy over a 11-year follow-up period in APOE-ε4 carriers

Published in Alzheimer's & Dementia, 2026

Lower cardiac output was associated with smaller brain volumes and subsequent ventricular enlargement in APOE-ε4 carriers. <DOI | PubMed>

Recommended citation: Moore, E. E., Zhang, P., Khan, O. A., Liu, D., Gupta, D. K., Pechman, K. R., Gifford, K. A., Landman, B. A., Hohman, T. J. and Jefferson, A. L. (2026). "Lower cardiac output is a risk factor for faster cerebral atrophy over a 11-year follow-up period in APOE-ε4 carriers." Alzheimer's & Dementia, 22(8), e71598. https://doi.org/10.1002/alz.71598

The role of vascular risk factors in white matter tract microstructure: a multi-cohort study in older adults

Published in Alzheimer's & Dementia, 2026

Across five cohorts, hypertension and heart disease showed the strongest and most widespread associations with white matter microstructure. <DOI | PubMed>

Recommended citation: LeFevre, J. D., Vyas, Y., Sathe, A., Shashikumar, N., Pechman, K. R., Yang, Y., Durant, A., Kanakaraj, P., Kim, M. E., Gao, C., Newlin, N. R., Ramadass, K., Khairi, N. M., Li, Z., Yao, T., Risacher, S. L., Zhang, P., Schilling, K. G., Lee, A. J., Brickman, A. M., Mayeux, R., Mez, J., Kukull, W., Biber, S. A., Landman, B. A., Bendlin, B. B., Johnson, S. C., Schneider, J., Barnes, L. L., Bennett, D. A., Saykin, A. J., Cuccaro, M. L., Hohman, T. J., Jefferson, A. L. and Archer, D. B., for ADNI, ADSP and ADSP-PHC (2026). "The role of vascular risk factors in white matter tract microstructure: a multi-cohort study in older adults." Alzheimer's & Dementia, 22(8), e71698. https://doi.org/10.1002/alz.71698

Increased neuroplastic activity in the pathogenesis of Alzheimer’s disease

Published in Alzheimer's & Dementia, 2025

In this study, we found that increased neuroplastic activity, measured by elevated CSF GAP-43 levels, in individuals with Alzheimer’s risk factors was associated with accelerated development of hallmarks of Alzheimer’s disease pathology. <DOI | PubMed>

Recommended citation: Bolton, C. J., Zhang, P., Wilhoite, S. R., Moore, E. E., Houston, M. L., Pechman, K. R., Dumitrescu, L., Peterson, A., Khan, O. A., Liu, D., Gifford, K. A., Blennow, K., Hohman, T. J., Zetterberg, H. and Jefferson, A. L. (2025). "Increased neuroplastic activity in the pathogenesis of Alzheimer's disease." Alzheimer's & Dementia, 21(11), e70897. https://doi.org/10.1002/alz.70897

Mild kidney dysfunction affects the predictive accuracy of blood-based biomarkers for neuropsychological and neuroimaging outcomes over a 9 year follow-up period

Published in Alzheimer's & Dementia, 2025

In this study, we found that mild kidney dysfunction significantly alters plasma Alzheimer’s biomarkers (e.g., NfL), thereby reducing their diagnostic accuracy and highlighting the need to account for renal function in clinical and research applications. <DOI | PubMed>

Recommended citation: Bolton, C. J., Bolton, C. J., Zhang, P., Nair, D., Liu, D., Davis, L. T., Pechman, K. R., Shashikumar, N., Wilhoite, S., Roby, D., Beeson, C., Komorowski, H., Gifford, K. A., Hohman, T. J., Blennow, K., Zetterberg, H. and Jefferson, A. L (2025). "Mild kidney dysfunction affects the predictive accuracy of blood-based biomarkers for neuropsychological and neuroimaging outcomes over a 9 year follow-up period." Alzheimer's & Dementia, 21(9), e70651. https://doi.org/10.1002/alz.70651

Cross-sectional and longitudinal associations of neighborhood disadvantage with fluid biomarkers of neuroinflammation and neurodegeneration

Published in Neurology, 2025

In this study, we found that neighborhood socioeconomic disadvantage, as measured by a higher Area Deprivation Index (ADI), was longitudinally linked to elevated blood and CSF biomarkers of neuroinflammation and neurodegeneration in older adults, suggesting social determinants may influence Alzheimer-related biology. <DOI | PubMed>

Recommended citation: Gogniat, M. A., Khan, O. A., Ratangee, B., Bolton, C. J., Zhang, P., Liu, D., Pechman, K. R., Yates, A., Gaynor, L. S., Eaton, J., Peterson, A., Gifford, K. A., Hohman, T. J., Blennow, K., Zetterberg, H. and Jefferson, A. L. (2025). "Cross-sectional and longitudinal associations of neighborhood disadvantage with fluid biomarkers of neuroinflammation and neurodegeneration." Neurology, 105(2), e213770. https://doi.org/10.1212/WNL.000000000021377

LC-MS/MS proteomics identifies plasma proteins related to cognition over 9-year follow-up

Published in Alzheimer's & Dementia, 2025

In this paper, we identified 10 plasma proteins whose baseline levels significantly predicted cognitive decline in specific domains: language (e.g., EGFR, RTN4RL2), processing speed (e.g., EGFR, NOMO2, CLEC3B), executive function (A1BG), and visuospatial skills (e.g., RTN4RL2, GALNT1, SERPINA4, SERPINA5, C8A, ALDOB); though not episodic memory. <DOI | PubMed>

Recommended citation: Adegboye, H. A., Patterson, K. L., Libby, J., Sun, Y., Zhang, P., Liu, D., Robb, W. H., Peterson, A. J., Cole, K. R., Arul, A. B., Oliver, N. C., Whitaker, M. D., Pechman, K. R., Dumitrescu, L., Bolton, C. J., Blennow, K., Zetterberg, H., Hohman, T. J., Robinson, R. A. S. and Jefferson, A. L. (2025). "LC-MS/MS proteomics identifies plasma proteins related to cognition over 9-year follow-up." Alzheimer's & Dementia, 21(6), e70276. https://doi.org/10.1002/alz.70276

Characterizing patterns of diffusion tensor imaging variance in aging brains

Published in Journal of Medical Imaging, 2024

In this paper, we analyze DTI data from 1035 subjects in the Baltimore Longitudinal Study of Aging, with ages ranging from 22.4 to 103 years old. We assessed the variance of DTI scalars within regions of interest (ROIs) defined by four segmentation methods and investigated the relationships between the variance and covariates, including baseline age, time from the baseline, motion and sex, among others. This work has provided a foundation for study planning to account for regional variations in metric variance. <DOI | medRxiv>

Recommended citation: Gao, C., Yang, Q., Kim, M. E., Khairi, N. M., Cai, L. Y., Newlin, N. R., Kanakaraj, P., Remedios, L. W., Krishnan, A. R., Yu, X., Yao, T., Zhang, P., Schilling, K. G., Moyer, D., Archer, D. B., Resnick, S. M., Landman, B. A., the Alzheimer's Disease Neuroimaging Initiative and the BIOCARD Study Team. (2024). "Characterizing patterns of diffusion tensor imaging variance in aging brains. "Journal of Medical Imaging, 11(4), 044007. https://doi.org/10.1117/1.JMI.11.4.044007

A strength and sparsity preserving algorithm for generating weighted, directed networks with predetermined assortativity

Published in Physica A: Statistical Mechanics and its Applications, 2024

In this paper, we proposed an efficient algorithm for generating weighted, directed networks with given assortativity measures. The determination of target networks was done by solving a linear programming problem, followed by a rewiring algorithm preserving node strenghts and network sparsity. The method implementation was done through Python. <DOI | ArXiv>

Recommended citation: Yuan, Y., Yan, J. and Zhang, P. (2024). "A strength and sparsity preserving algorithm for generating weighted, directed networks with predetermined assortativity. "Physica A: Statistical Mechanics and its Applications, 638, 129634. https://doi.org/10.1016/j.physa.2024.129634

Variational Bayesian inference for bipartite mixed-membership stochastic block model with applications to collaborative filtering

Published in Computational Statistics & Data Analysis, 2023

In this paper, we proposed a novel mixed-membership stochastic block model for bipartite networks. The model was derived analytically, and a variational Bayesian algorithm was introduced for inference. Extensive simulations were conducted for empirical justification. The model was applied to a MovieLens dataset for a real data application. <DOI | ArXiv>

Recommended citation: Liu, J., Ye, Z., Chen, K. and Zhang, P. (2024). "Variational Bayesian inference for bipartite mixed-membership stochastic block model with applications to collaborative filtering." Computational Statistics & Data Analysis, 189, 107836. https://doi.org/10.1016/j.csda.2023.107836

A mixed-membership model for social network clustering

Published in Journal of Data Science, 2023

In this paper, we proposed a simple mixed-membership model for social network clustering, where a flexible function was adopted to measure the affinities among social network entites. The inference was done using an MCMC algorithm. The performance of the proposed algorithm was evaluated by applying to the Zachary club data and the bottlenose dolphin network data.

Recommended citation: Ouyang, G., Dey, D. K. and Zhang, P. (2023). "A mixed-membership model for social network clustering." Journal of Data Science, 21(3), 508--522. https://doi.org/10.6339/23-JDS1109

On several properties of a class of hybrid recursive trees

Published in Methodology and Computing in Applied Probability, 2023

In this paper, we considered a class of random recursive trees whose evolution integrated uniform and preferential attachements, namely hybrid recursive trees. We specifically investigated the degree profile, the degree distribution, the number of leaves and the Zagreb index of the proposed model.

Recommended citation: Zhang, P. (2023). "On Several properties of a class of hybrid recursive trees." Methodology and Computing in Applied Probability, 25(1), 16. https://doi.org/10.1007/s11009-023-09988-z

Incorporating auxiliary information in betweenness measure for input–output networks

Published in Physica A: Statistical Mechanics and its Applications, 2022

In this paper, we proposed a novel betweenness measure incorporating auxiliary information in the computation. The proposed measure has a practical economic interpretation, and helps accurately identify key sectors of input-output netowrks, which provides insights for policy makers. The implementation of our mathod is publicly available in an R package ionet.

Recommended citation: Xiao, S., Yan, J. and Zhang, P. (2022). "Incorporating auxiliary information in betweenness measure for input–output networks." Physica A: Statistical Mechanics and its Applications, 607, 128200. https://doi.org/10.1016/j.physa.2022.128200

The degree Gini index of several classes of random trees and their poissonized counterparts—Evidence for duality

Published in Journal of Stochastic Analysis, 2022

In this paper, we provided some evidence showing duality between discrete-time random trees and their poissonized (continuous-time) counterparts. Specifically, we looked into the limiting degree Gini indices of binary search trees, binary pyramids and random caterpillars.

Recommended citation: Domicolo, C., Zhang, P. and Mahmoud, H. (2022). "The degree Gini index of several classes of random trees and their poissonized counterparts---Evidence for duality. "Journal of Stochastic Analysis, 3(4), 1. https://doi.org/10.31390/josa.3.4.01

Generating directed networks with predetermined assortativity measures

Published in Statistics and Computing, 2022

In this paper, we proposed an efficient algorithm, called DiDPR, for generating directed networks with predetermined (directed) assortativity measures. The performance assessment of the proposed algorithm was done through extensive simulations and the application to a Facebook wall post social network. The implementation of DiDPR is available in an R package wdnet.

Recommended citation: Wang, T., Yan, J., Yuan, Y. and Zhang, P. (2022). "Generating directed networks with predetermined assortativity measures." Statistics and Computing, 91(5), 91. https://doi.org/10.1007/s11222-022-10161-8

Functional data analysis: An application to COVID‐19 data in the United States in 2020

Published in Quantitative Biology, 2022

In this paper, we conducted an analysis of the COVID-19 data in the United States in 2020 via functional data analysis methods, including functional principal component analysis methods, functional canonical correlation analysis methods, an EM based clustering algorithm and a functional time series model used for forecasting.

Recommended citation: Tang, C., Wang, T. and Zhang, P. (2022). "Functional data analysis: An application to COVID‐19 data in the United States in 2020." Quantitative Biology, 10(2), 172--187. https://doi.org/10.15302/J-QB-022-0300

Appropriateness of applying cerebrospinal fluid biomarker cutoffs from Alzheimer’s disease to Parkinson’s disease

Published in Journal of Parkinson's Disease, 2022

In this paper, we evaluated whether cerebrospinal fluid (CSF) biomarker cutoffs established for Alzheimer’s disease (AD), specifically amyloid-ß 1-42 (Aß42), total tau (t-tau), phosphorylated tau (p-tau), and the ratios t-tau/Aß42 and p-tau/Aß42, are appropriate when applied to Parkinson’s Disease (PD) patients using the Parkinson’s Progression Markers Initiative cohort. Amyloid PET imaging and longitudinal cognitive outcomes were used as reference standards. We found that the optimal Aß42 cutoff in the PD cohort was higher than the AD-derived value, while the cutoffs for t-tau/Aß42 and p-tau/Aß42 were significantly lower than in AD, with non-overlapping confidence intervals. Similarly, optimal thresholds for t-tau and p-tau to predict cognitive decline in PD were significantly lower than AD cutoffs. The results suggest that AD-based CSF biomarker thresholds may not generalize to PD populations, likely reflecting the impact of disease-specific pathologies such as alpha-synuclein in shaping biomarker distributions.

Recommended citation: Weinshel, S., Irwin, D. J., Zhang, P., Weintraub, D., Shaw, L. M., Siderowf, A., and Xie, S. X. (2022). "Appropriateness of applying cerebrospinal fluid biomarker cutoffs from Alzheimer's disease to Parkinson's disease." Journal of Parkinson's Disease, 12(4), 1155--1167. https://doi.org/10.3233/JPD-212989

Directed hybrid random networks mixing preferential attachment with uniform attachment mechanisms

Published in Annals of the Institute of Statistical Mathematics, 2022

In this paper, we considered a directed hybrid random network mixing preferential attahcment (PA) rules with uniform attachment (UA) rules. We proved that this class of hybrid networks would have lighter distributional tails than directed PA networks. For inference, two parameter estimation schemes were developed, and justified by simulations. A real network data application showed that the proposed network model provided a better fit than pure PA model.

Recommended citation: Wang, T. and Zhang, P. (2022). "Directed hybrid random networks mixing preferential attachment with uniform attachment mechanisms." Annals of the Institute of Statistical Mathematics, 74(5), 957--986. https://doi.org/10.1007/s10463-022-00827-5

PageRank centrality and algorithms for weighted, directed networks

Published in Physica A: Statistical Mechanics and its Applications, 2021

In this paper, we propose a measure called weighted PageRank (WPR) for weighted, directed networks, with possible non-uniform node-specific information as prior. Through simulations and applications to World Input-Output Networks, we have found the proposed measure outperforms classical PageRank.

Recommended citation: Zhang, P., Wang, T. and Yan, J. (2022). "PageRank centrality and algorithms for weighted, directed networks." Physica A: Statistical Mechanics and its Applications, 586, 126438. https://doi.org/10.1016/j.physa.2021.126438

Regional and sectoral structures of the Chinese economy: A network perspective from multi-regional input-output tables

Published in Physica A: Statistical Mechanics and its Applications, 2021

In this paper, we utilize network analysis tools to analyze the regional and sectoral structure of the Chinese economy with the multi-regional input-output tables of China in 2007 and 2012. We respectively carry out global, regional and local analyses to uncover a few interesting and telling insights.

Recommended citation: Wang, T., Xiao, S., Yan, J. and Zhang, P. (2021). "Regional and sectoral structures of the Chinese economy: A network perspective from multi-regional input–output tables." Physica A: Statistical Mechanics and its Applications, 581, 126196. https://doi.org/10.1016/j.physa.2021.126196

Assortativity measures for weighted and directed networks

Published in Journal of Complex Networks, 2021

In this paper, we propose a class of assortativity measures for weighted, directed networks. Through simulation studies and applications to World Input-Output Tables, we find that the proposed measures outperform the classical counterparts without accounting for edge weights and directions. The implementation of the proposed measures is is publicly available in a R package wdnet.

Recommended citation: Yuan, Y., Yan, J. and Zhang, P. (2021). "Assortativity measures for weighted and directed networks." Journal of Complex Networks, 9(2), cnab017. https://doi.org/10.1093/comnet/cnab017

Investigating several fundamental properties of random lobster trees and random spider trees

Published in Methodology and Computing in Applied Probability, 2021

In this paper, we uncover the structures of random lobster and spider trees. Specifically, we investigate the random lobster trees that grow in two different manners. For random spider trees, we characterize the asymptotic distriubtion of the number of leaves as well as two kinds of topological indices.

Recommended citation: Ren, Y., Zhang, P. and Dey, D. K. (2022). " Investigating several fundamental properties of random lobster trees and random spider trees." Methodology and Computing in Applied Probability, 24(1), 431--447. https://doi.org/10.1007/s11009-021-09863-9

Characterizing several properties of high-dimensional random Apollonian networks

Published in Journal of Complex Networks, 2020

In this paper, we investigate several properties of high-dimensional random Apollonian networks, including two types of degree profiles, the small-world effect, sparsity and three distance-based metrics.

Recommended citation: Zhang, P. (2020). "Characterizing several properties of high-dimensional random Apollonian networks." Journal of Complex Networks, 8(4), cnaa038. https://doi.org/10.1093/comnet/cnaa038

Limbic-predominant age-related TDP-43 encephalopathy differs from frontotemporal lobar degeneration

Published in Brain, 2020

TAR-DNA binding protein-43 (TDP-43) proteinopathy has been seen in multiple brain diseases. In this paper, we combine both cases and neuropathologists’ diagnoses from two research centres—University of Pennsylvania and University of Kentucky. The study is designed to compare neuropathological findings between frontotemporal lobar degeneration with TDP-43 (FTLD-TDP) and limbic-predominant, age-related TDP-43 encephalopathy (LATE).

Recommended citation: Robinson, J. L., Porta, S., Garrett, F. G., Zhang, P., Xie, S. X., Suh, E., Van Deerlin, V. M., Abner, E. L., Jicha, G. A., Barber, J. M., Lee, V. M.-Y., Lee, E. B., Trojanowski, J. Q. and Nelson, P. T. (2020). "Limbic-predominant age-related TDP-43 encephalopathy differs from frontotemporal lobar degeneration." Brain, 143(9), 2844--2857. https://doi.org/10.1093/brain/awaa219

Meta-analysis of several epidemic characteristics of COVID-19

Published in Journal of Data Science, 2020

In this paper, we utilize meta-analysis to study several epidemic characteristics of commont interest with regard to the COVID-19: the basic reproduction number, the incubation period, the serial interval and the epidemic doubling time.

Recommended citation: Zhang, P., Wang T. and Xie, S. X. (2020). "Meta-analysis of several epidemic characteristics of COVID-19." Journal of Data Science, 18(3), 536--549. https://doi.org/10.6339/JDS.202007_18(3).0019

Logistic quantile regression for bounded outcomes using a family of heavy-tailed distributions

Published in Sankhya B, 2020

In this paper, we proposed a robust logistic quantile regression (QR) model by using a logit link function along an EM-based algorithm. The QR model was built on a generalized class of skewed distributions. The proposed method was compared with a nonparametric competing alternative.

Recommended citation: Galarza, C. E., Zhang, P. and Lachos, V. H. (2020). "Logistic quantile regression for bounded outcomes using a family of heavy-tailed distributions." Sankhya B, https://doi.org/10.1007/s13571-020-00231-0. https://doi.org/10.1007/s13571-020-00231-0

On nodes of small degrees and degree profile in preferential dynamic attachment circuits

Published in Methodology and Computing in Applied Probability, 2020

In this paper, we investigated two properties of a class of preferential attachment (PA) networks evolving in a dynamic manner: the joint distribution of nodes of small degrees and the degree profile. The primary methods for the analysis included martingale theory, Pólya urns and stochastic recurrences.

Recommended citation: Zhang, P. and Mahmoud, H. M. (2020). "On nodes of small degrees and degree profile in preferential dynamic attachment circuits." Methodology and Computing in Applied Probability, 22(2), 625--645. https://doi.org/10.1007/s11009-019-09726-4

On several properties of a class of preferential attachment trees—plane-oriented recursive trees

Published in Probability in the Engineering and Informational Sciences, 2020

In this paper, we look into the degree profile of plane-oriented recursive trees (PORTs), a class of random trees presenting the feature of preferential attachment (PA). Besides, we study the Zagreb index of the PORTs, by computing the first two moments. Lastly, we determine degree distribution of the PORTs growing in continuous time where a poissonization-based embedding has been adapted.

Recommended citation: Zhang, P. (2020). "On several properties of a class of preferential attachment trees---plane-oriented recursive trees." Probability in the Engineering and Informational Sciences, 35(4), 839--857. https://doi.org/10.1017/S0269964820000261

Distributions in the constant-differentials Pólya process

Published in Statistics & Probability Letters, 2019

In this paper, we study a class of unbalanced constant-differentials Pólya processes on two colors. We show that the asymptotic distribution of the number of white (blue) balls depneds on the diferential index, but not on the initial conditions. The result is obtained by an analytic approach utilizing partial differential equations.

Recommended citation: Mahmoud, H. M. and Zhang, P. (2020). "Distributions in the constant-differentials Pólya process." Statistics & Probability Letters, 156, 108592. https://doi.org/10.1016/j.spl.2019.108592

Clique-based method for social network clustering

Published in Journal of Classification, 2019

In this paper, we developed a clique-based method for social network clustering. A new index evaluating the quality of clustering results was proposed alongside an algorithm for inference. A statistical procedure of controlling under- and over-clustering was practically introduced. Simulation studies were carried out using stochastic blockmodels.

Recommended citation: Ouyang, G., Dey, D. K. and Zhang, P. (2020). "Clique-based method for social network clustering." Journal of Classification, 37(1), 254--274. https://doi.org/10.1007/s00357-019-9310-5

The degree profile and Gini index of random caterpillar trees

Published in Probability in the Engineering and Informational Sciences, 2018

In this paper, we investigated the degree profile and the Gini index of two classes of random caterpillars evolving in different manners: uniform and preferential attachment (PA). The primariy method used in the analysis included stochastic recurrences, generalized Pólya urns and some combinatorial computing techniques.

Recommended citation: Zhang, P. and Dey, D. K. (2019). "The degree profile and Gini index of random caterpillar trees." Probability in the Engineering and Informational Sciences, 33(4), 511--527. https://doi.org/10.1017/S0269964818000475

Characterizations of asymptotic distributions of continuous-time Pólya processes

Published in Communications in Statistics---Theory and Methods, 2018

In this paper, we studied a general class of poissonized (tenable and balanced) urns. We characterized the asymptotic behavior of the processes by solving a partial differential equation governing the processes. We also conducted an analogous analysis of a class of processes associated with randomized replacement matrix. <DOI | ArXiv>

Recommended citation: Chen, C. and Zhang, P. (2019). "Characterizations of asymptotic distributions of continuous-time Pólya processes. "Communications in Statistics---Theory and Methods, 48(21), 5308--5321. https://doi.org/10.1080/03610926.2018.1510005

Scan statistics on graphs and networks

Published in Handbook of Scan Statistics, 2017

This is an article surveying scan statistics on graphs and networks. Theories and methodologies of constructing scan statistics for both static and dynamic graphs are reviewed. Several popular convex approximation algorithms for computing scan statistics are reviewed as well.

Recommended citation: Zhang, P. and Glaz, J. (2018). "Scan statistics on graphs and networks." In Glaz, J. and Koutras, M. V. (Eds.) Handbook of Scan Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8414-1_43-1

Distributions in a class of Poissonized urns with an application to Apollonian networks

Published in Statistics & Probability Letters, 2016

In this paper, we studied a class of Pólya processes underlying terminal nodes in a random Apollonian network (RAN). The first two moments were computed exactly by solving a set of ordinary differential equations. Additionaly, we exploited classical methods of branching processes to derive the asymptotic results.

Recommended citation: Zhang, P. and Mahmoud, H. M. (2016). "Distributions in a class of Poissonized urns with an application to Apollonian networks." Statistics & Probability Letters, 115, 1--7. https://doi.org/10.1016/j.spl.2016.03.023

The degree profile and weight in Apollonian networks and k-trees

Published in Advances in Applied Probability, 2016

In this paper, we investigated two properties of high-dimensional random Apollonian networks (RANs): the degree profile and a novel topological index called total weight. The primary methods for the analysis included martingale theory, Pólya urns and stochastic recurrences.

Recommended citation: Zhang, P. and Mahmoud, H. M. (2016). "The degree profile and weight in Apollonian networks and k-trees." Advances in Applied Probability, 48(1), 163--175. https://doi.org/10.1017/apr.2015.11

On terminal nodes and the degree profile of preferential dynamic attachment circuits

Published in Proceedings of the Thirteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), 2016

In this paper, we investigate terminal nodes and the degree profile in preferential dynamic attachment circuits. We show that the number of terminal nodes followed a Gaussian law asymptotically. A generalized Pólya urn model is used to study the exact distribution of the degree of a specific node in the circuit.

Recommended citation: Zhang, P. (2016). "On terminal nodes and the degree profile of preferential dynamic attachment circuits." In 2016 Proceedings of the Thirteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Arlington, VA, 80--92. SIAM, Philadelphia, PA. https://doi.org/10.1137/1.9781611974324.9

Explicit characterization of moments of balanced triangular Pólya urns by an elementary approach

Published in Statistics & Probability Letters, 2014

In this paper, we propose an elementary approach to studying two-color urn model. The dynamic of the urns is characterized via the moments. The exact moments include Stirling numbers of the second second kind. The asymptoic moments are derived as well.

Recommended citation: Zhang, P., Chen, C and Mahmoud, H. M. (2015). "Explicit characterization of moments of balanced triangular Pólya urns by an elementary approach." Statistics & Probability Letters, 96, 149--153. https://doi.org/10.1016/j.spl.2014.09.016