Laplace’s Equation and the Fundamental Solution of the Poisson Equation
Published:
The radial harmonic solution, the fundamental solution of Laplace’s equation, and a proof that $\Phi * f$ solves the Poisson equation.
Posts by Collection
notes
A Working Tutorial on Diffusion Models
Published:
Diffusion from the ground up: VAE/ELBO, DDPM, score matching, DSM/Tweedie, SDEs, Fokker–Planck, and Anderson’s reverse-time equation.
portfolio
publications
Graphs-of-Constraints Model Predictive Control for Reactive Multi-agent Task and Motion Planning
A. Manganaris, J. Lu, A. H. Qureshi, and S. Jagannathan. (2026). "Graphs-of-Constraints Model Predictive Control for Reactive Multi-agent Task and Motion Planning." IEEE/RAS International Conference on Robotics and Automation (ICRA).
Sequences of interdependent geometric constraints are central to many multi-agent Task and Motion Planning (TAMP) problems. However, existing methods for handling such constraint sequences struggle with partially ordered tasks and dynamic agent assignments. They typically assume static assignments and cannot adapt when disturbances alter task allocations. To overcome these limitations, we introduce Graph-of-Constraints Model Predictive Control (GoC-MPC), a generalized sequence-of-constraints framework integrated with MPC. GoC-MPC naturally supports partially ordered tasks, dynamic agent coordination, and disturbance recovery. By defining constraints over tracked 3D keypoints, our method robustly solves diverse multi-agent manipulation tasks-coordinating agents and adapting online from visual observations alone, without relying on training data or environment models. Experiments demonstrate that GoC-MPC achieves higher success rates, significantly faster TAMP computation, and shorter overall paths compared to recent baselines, establishing it as an efficient and robust solution for multi-agent manipulation under real-world disturbances.
Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion
P. Jutras-Dubé, P. Pynadath, J. Lu, Y. Gao, and R. Zhang. (2026). "Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion." arXiv preprint arXiv:2607.10951.
Sticky Jump Diffusions (SJDs) are continuous-time Markov processes on R^d whose discrete anchors are token embeddings. In the forward process, anchors release mass at a hazard rate that diffuses in continuous space; time reversal pairs a score-driven SDE with a sticky jump kernel governed by flux balance. Scores and reverse hazards are estimated through Denoising Hazard Matching using simulation-free cross-entropy training. The framework unifies masked, continuous, and hybrid diffusion as limiting cases and explains features each treats as given. Beyond these limits, the unsticking kernel becomes a design space: cross-position blending corrupts each position toward a blend of its neighbors’ clean values or embeddings, improving results on CIFAR-10, Text8, and Sudoku.
talks
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Teaching experience 2
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.