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Research

Handwriting by Stanley Nicholson

I am broadly interested in applied probability, but I specialize in stochastic analysis and interacting particle systems, particularly limit theory and adjacent graph-theoretic concerns. I’ve also applied probabilistic methods to machine learning, signal processing, mathematical biology, quantum networks, and quantum algorithms.

Below is a selected list of my published work, organized in terms on topics (coauthors listed in alphabetical order unless specified). For a complete, chronological ordered (and automatically updated) list, see my Google Scholar profile.

Machine Learning and signal processing

• A variational framework for residual-based adaptivity in neural PDE solvers and operator learning (with Juan D. Toscano, Vivek Oommen, Jerome Darbon, George Em Karniadakis). NPJ Artifical Intelligence (2026). Journal. ArXiv.

• Explicitly solvable continuous-time inference for partially-observed Markov processes (with Andrew W. Eckford, Alexander G. Strang, and Peter J. Thomas). IEEE Transactions on Signal Processing (2022). Journal. Arxiv.

Mathematical Biology

• Capacity of a class of fully observed multistate Poisson-type signal transduction channels (with Andrew W. Eckford, and Peter J. Thomas). IEEE International Symposium on Information Theory (2025). Conference.

Quantum Algorithms and Networks

• Inferring quantum network topology using local measurements (with Brian Doolittle, Eric Chitambar, Jeffrey Larson, and Zain H. Saleem). PRX Quantum (2023). Journal. Arxiv.

• Quantum circuit cutting for classical shadows (with Michael A. Perlin and Zain H. Saleem). ACM Transactions on Quantum Computing(2024). Journal. Arxiv

• Online detection of golden circuit cutting points (with Ethan Hansen, Shuai Xu, and others). IEEE Conference on Quantum Computing and Engineering (2023). Conference. Arxiv.