Howdy, I'm Nate! 👋 I thrive as a generalist, immersing myself in the vast world where mathematics, programming, machine learning, and generative AI converge. My passion lies in mastering new domains, solving complex problems, effectively communicating ideas across technical and general audiences, and mentoring the next generation of innovators. The highlight of my day is engaging with domain experts, aiding them in their current challenges while always envisioning what I could build next to extend my impact even further. 🚀

Interests:

• Large Language Models, Generative AI, Natural Language Processing, Information Retrieval, Spectral and Algebraic Graph Theory, Matrix Analysis, Machine Learning, Deep Learning, ML Applications (to e-Discovery and many other domains)

Publications

• Artificial Intelligence in Document Review: Statistically Defending the Process and Results of E-Discovery Workflows (with A. Ahmadia, M. Reiber, C. Roberts, and C. Traylor), Journal of Technology Law & Policy, 30(2) (2026).
• Beyond the Bar: Generative AI as a Transformative Component in Legal Document Review (with R. Omrani, E. Yang, E. Curtin, T. Emory, L. Gray, J. Pickens, C. Traylor, S. Underwood, D. Lewis, A. Ahmadia), 2024 IEEE International Conference on Big Data (BigData), (2024), 4779-4788.
• Spectra of complex unit hypergraphs (with Raffaella Mulas), The Art of Discrete and Applied Mathematics, 7(3), (2024).
• Spectra of quaternion unit gain graphs (with Francesco Belardo, Maurizio Brunetti, Nolan J. Coble, and Howard Skogman), Linear Algebra Appl., 632 (2022), 15-49.
• Balancedness and the least Laplacian eigenvalue of some complex unit gain graphs (with Francesco Belardo and Maurizio Brunetti), Discussiones Mathematicae Graph Theory 40 (2020), 417-433.
• Lower bounds for the Laplacian spectral radius of an oriented hypergraph (with Ouail Kitouni), Australas. J. Combin., 574(3) (2019), 408-422
• Spectra of cycle and path families of oriented hypergraphs (with Luke Duttweiler), Linear Algebra Appl., 578 (2019), 251-271.
• A Connection Between Hadamard Matrices, Oriented Hypergraphs and Signed Graphs (with Howard Skogman), Linear Algebra Appl., 529 (2017), 115-125.
• Oriented gain graphs, line graphs and eigenvalues, Linear Algebra Appl., 506 (2016), 316-328.
• Intersection graphs of oriented hypergraphs and their matrices, Australas. J. Combin., 65(1) (2016) 108-123.
• Spectral properties of oriented hypergraphs, Electron. J. Linear Algebra., 27 (2014) 373-391.
• An oriented hypergraphic approach to algebraic graph theory (with Lucas Rusnak), Linear Algebra Appl., 437 (2012) 2262-2270.
• Spectral properties of complex unit gain graphs, Linear Algebra Appl., 436 (2012), 3165-3176.

Patents

• Systems and Methods for Simulating a Deposition to Identify Objects to Pre-Load into a Cache of a Client Device (with A. Ahmadia, S. Anand, T. Cooray, and G. Shao), U.S. Patent Application Pub. No. 20260203843, filed January 14, 2026.
• Systems and Methods for Updating Fact Objects Following a Deposition Event (with A. Ahmadia, S. Anand, T. Cooray, and G. Shao), U.S. Patent Application Pub. No. 20260203273, filed January 14, 2026.
• Systems and Methods for Real-Time Analysis and Response Generation to Deposition Data and a Deposition Plan (with A. Ahmadia, S. Anand, T. Cooray, and G. Shao), U.S. Patent Application Pub. No. 20260203844, filed January 14, 2026.
• Systems and Methods for Real-Time Analysis and Response Generation to Deposition Data (with A. Ahmadia, S. Anand, T. Cooray, and G. Shao), U.S. Patent Application Pub. No. 20260203845, filed January 14, 2026.
• Systems and Methods for Identifying a Seed Set of Documents from a Corpus of Documents (with A. Ahmadia and E. M. Curtin), U.S. Patent Application Pub. No. 20260141008, filed November 12, 2025.
• Systems and Methods for Generating Fact Objects from a Corpus of Documents (with A. Ahmadia), U.S. Patent Application Pub. No. 20260134023, filed November 12, 2025.
• Systems and Methods for Prompt-Based Queues for Active Learning (with A. Ahmadia, M. Martinez, E. Tropiano, and E. Curtin), U.S. Patent Application Pub. No. 20250322306, filed February 12, 2025.
• Systems and Methods for Generating Initial Prompt Criteria (with A. Ahmadia, M. Martinez, E. Tropiano, and E. Curtin), U.S. Patent Application Pub. No. 20250258874, filed February 12, 2025.
• Systems and Methods for Iteratively Updating Classification Prompts (with A. Ahmadia, M. Martinez, E. Tropiano, and E. Curtin), U.S. Patent Application Pub. No. 20250258873, filed February 12, 2025.
• Systems and Methods for Prompt Tuning Based on Document Classification (with A. Ahmadia, M. Martinez, E. Tropiano, and E. Curtin), U.S. Patent Application Pub. No. 20250258872, filed February 12, 2025.
• Systems and Methods for Updating a Validation Sample (with A. Ahmadia, M. Martinez, E. Tropiano, and E. Curtin), U.S. Patent Application Pub. No. 20250258871, filed February 12, 2025.
• Systems and Methods for Prompt Self-Optimization (with A. Ahmadia, M. Martinez, E. Tropiano, and E. Curtin), U.S. Patent Application Pub. No. 20250258870, filed February 12, 2025.
• Systems and Methods for Classification Explainability (with A. Ahmadia, M. Martinez, E. Tropiano, and E. Curtin), U.S. Patent Application Pub. No. 20250258869, filed February 12, 2025.
• Systems and Methods for Using Synthetic Data to Train Machine Learning Models (with E. Curtin, A. Ahmadia, and E. Tropiano), U.S. Patent Application Pub. No. 20240354648, filed April 19, 2024.

Thesis

• Gain Graphs, Group-Oriented Hypergraphs, and Matrices, Ph.D. Thesis, Binghamton University, 2012.
Advisor: Thomas Zaslavsky.

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