Open and completed research requests

This project investigates whether real-world lottery draws deviate from ideal uniform randomness due to physical implementation effects such as ball weight, wear, machine mechanics, or procedural conditions. The approach combines number-theoretic feature design with statistical hypothesis testing and predictive modeling on historical draw data to detect persistent, reproducible structure. Rather than assuming dependence across draws, we explicitly test independence, stationarity, and mechanism-specific bias using both global and time-local analyses. The expected impact is a rigorous framework for distinguishing true mechanical bias from random fluctuation, with reproducible methods that can be applied across lottery systems.

Fourier transformation remains a core primitive in scientific computing, signal processing, and ML systems, but practical performance and accuracy depend heavily on algorithm and hardware choices. This project will build a reproducible benchmark framework to compare modern Fourier transformation implementations across representative workloads (1D/2D/3D, real/complex, varying sizes, and precision modes). We will evaluate both numerical fidelity and system-level efficiency to identify configuration-specific SOTA candidates rather than a one-size-fits-all winner. The expected impact is a decision guide and open benchmark suite that helps researchers and engineers select the best Fourier pipeline for their constraints.

Robust dynamic operating envelopes (RDOEs) solve the problem of secure allocation of latent network capacity to flexible distributed energy resources (DER) in unbalanced distribution networks. As the computational complexity of RDOEs is much higher than that of dynamic operating envelopes (DOEs), which disregard uncertainties in network parameters and DER capacity utilisation, existing approaches to computing RDOEs have relied on linearised unbalanced three-phase optimal power flow (UTOPF) models to numerate the network feasible region approximately. The use of linearised models, however, risks producing RDOEs that undermine network integrity due to inherent errors in the approximation. This letter presents a practical sensitivity-filtering technique to simplify RDOE numerical computation based on non-convex UTOPF formulations. The accuracy and efficiency of the proposed approach are demonstrated on RDOE allocation with various fairness metrics by testing on representative Australian distribution networks.