Complex image mapping
Published:
Warping images through complex-valued functions: each pixel at x + yi moves to f(x + yi).
Posts by Collection
portfolio
Social platform with an LLM assistant
Published:
Full-stack social platform with face matching, retrieval-backed chat, and Spark-based feed ranking.
C2NN: a C-to-neural-network compiler
Published:
An LLVM-based compiler that lowers C programs into equivalent neural networks.
LLM agent for FPGA design (Concurrent EDA)
Published:
An agent that runs the FPGA loop end to end: HDL generation, synthesis, optimization.
publications
Application of Machine Learning for Assessing Movement Disorders
Published in New Jersey Governor's School in the Sciences (student report), 2022
Student research report (NJ Governor's School in the Sciences) on using ML to detect walking irregularities.
Root Bounds for Chain Polynomials Beyond the Cohen–Macaulay World
Published in Preprint, submitted to the Electronic Journal of Combinatorics, 2026
All real roots of the chain polynomial of every finite graded poset lie in [−4, 0]. The proof replaces shellability and h-vectors with a sign condition on a matrix inverse.
Recommended citation: P. Dugan. "Root bounds for chain polynomials beyond the Cohen–Macaulay world." Preprint, 2026.
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talks
teaching
Teaching Assistant, CIS 1600: Mathematical Foundations of Computer Science
Undergraduate course, University of Pennsylvania, Department of Computer and Information Science, 2024
TA for CIS 1600 (discrete mathematics) on Professor Rajiv Gandhi’s staff, Fall 2024 to present.