My research addresses computational, mathematical, and statistical problems in the study of complex systems. My interests include network data science, dynamical models of social structures, and data science applications supporting equity and sustainability.

Methods of Network Data Science

How do we analyze and learn from network data? I build mathematical foundations for network data science algorithms, with recent focus on networks of higher-order interactions. Much of my work is devoted to developing novel random graph models and applying them in algorithms. Doing so often requires tools from probability, optimization, combinatorics, and random matrix theory.

Nonbacktracking spectral clustering of nonuniform hypergraphs
PSC, Nicole Eikmeier, and Jamie Haddock
SIAM Journal on Mathematics of Data Science (2023)

Generative hypergraph clustering: from blockmodels to modularity
PSC, Nate Veldt, and Austin Benson
Science Advances (2021)

Configuration models of random hypergraphs
Journal of Complex Networks (2020)

Moments of uniformly random multigraphs with fixed degree sequences
SIAM Journal on Mathematics of Data Science (2020)

Annotated hypergraphs: models and applications
PSC and Andrew Mellor
Applied Network Science (2020)

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Models of Polarization, Hierarchy, and Inequality

Human and animal societies are structured by persistent hierarchies, inequalities, and divisions. Dynamical and statistical models can help us understand the extent of these structures, how they form, and under what conditions they persist. I am especially interested in the role of social feedback loops in reinforcing these structures.

Emergence of polarization in a sigmoidal bounded-confidence model of opinion dynamics
Heather Zinn Brooks, PSC, and Mason Porter
arXiv (2023)

Emergence of hierarchy in networked endorsement dynamics
Mari Kawakatsu, PSC, Nicole Eikmeier, and Dan Larremore
Proceedings of the National Academy of Sciences (2021)
  • Commentary by Simon DeDeo and Elizabeth Hobson
  • Explainer post on SIAM News blog

  • Local symmetry and global structure in adaptive voter models
    PSC and Peter Mucha
    SIAM Journal on Applied Mathematics (2021)

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    Data Science and Social Responsibility

    I also use my skills and resources in the service of equity, sustainability, and justice. My efforts here includes both the development of novel methods for social data analysis and work on activist data science projects. I pursue some of this work as a Partner at QSIDE, the Institute for the Quantitative Study of Inclusion, Diversity, and Equity.

    Data science and social justice in the mathematics community
    Quindel Jones, Andrés R. Vindas Meléndez, Ariana Mendible, Manuchehr Aminian, Heather Zinn Brooks, Nathan Alexander, Carrie Diaz Eaton, and PSC
    Notices of the American Mathematical Society (2023)

    Persons charged with violations of 21 U.S.C. §846: Poverty, unemployment, education, and sentences.
    PSC, Manuchehr Aminian, Carlos Paniagua, and Jude Higdon
    Part of an amicus brief in Rodriguez-Rivera v. United States, U.S. Supreme Court case 21-143 (2021)

    Space-based observational constraints on NO₂ air pollution inequality from diesel traffic in major U.S. cities
    Mary Angelique Demetillo, Colin Harkins, Brian McDonald, PSC, Kang Sun, and Sally Pusede
    Geophysics Review Letters (2021)
  • Writeup in Chemical and Engineering News

  • Structure and information in spatial segregation
    Proceedings of the National Academy of Sciences (2017)

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    Key Collaborators

    Student Research

    If you are a Middlebury student interested in working with me as a research collaborator, I have a whole list of FAQs just for you!

    Other Work

    The research on this page is the best description of my current interests and activities. For my complete research record, see my Google Scholar page.