G

Gaussian Processes

An interactive living book and software repository dedicated to reconstructing Archimedes' circle measurement ("Circvli Dimensio") using original geometric proportions. Leveraging SageMath for symbolic validation and Python/Perl for high-precision numerical computation via decimal/big-number libraries, this project bypasses modern algebraic transformations to prove the flawless accuracy of antike geometric frameworks.

It now expands this foundation into a unified algebraic framework capable of handling higher-order transcendental structures up to \pi^4 and 1/\pi^4, including additive transcendental invariants like \log(2). By introducing a specialized mathematical Gain Function, the engine dynamically bridges ancient geometry with hyper-convergent modern infinite series—such as those of Ramanujan, the Chudnovsky brothers, and the 2024 Saha-Sinha string theory iterations. Through precise lambda (\lambda) parameter tracking to bypass critical systemic singularities and prevent degeneration into the slower Madhava series, the optimized, dual-action polygon generators achieve absolute numeric stability, delivering hundreds of flawless decimal places without relying on circular trigonometric functions.

And much more!

CTA is a testing environment for online heterogenous task assignment approaches which involve representation of worker-task pairs as noisy functions.

"n" dimensional input with "m" objectives example of a Pareto front with the BOSS code. In these examples we reproduce the pareto front as produced by mathlab in the link below "https://www.mathworks.com/help/gads/pareto-front-for-two-objectives.html" For 3D inputs and 3 objectives, we try to reproduce these results The difference in these methods is that here we calculate the pareto front using GP functions with an RBF kernel.

Data simulations for Gaussian Process Classification of data from sensors attached to a hypothetical machine.

Source Code for Gabler et al. "Bayesian Optimization with Unknown Constraints in Graphical Skill-Models for Compliant Manipulation Tasks Using an Industrial Robot", Frontiers in Robotics and AI, 2022

Learning in the Wild with Incremental Skeptical Gaussian Processes

This is a pilot project for a future iteration of The Alice Challenge: remote control of an ultracold atoms experiment by experts and citizen scientist. Scientific paper available here: https://www.pnas.org/content/115/48/E11231

Miscellaneous Machine Learning Example Code for sci-kit learn, refactored to PEP8 style

Scalable Gaussian processes in TensorFlow