Formal verification is a promising method for producing reliable software, but the difficulty of manually writing verification proofs severely limits its utility in practice. Recent methods have automated some proof synthesis by guiding a search through the proof space using a theorem prover. Unfortunately, the theorem prover provides only the crudest estimate of progress, resulting in effectively undirected search. To address this problem, we create QEDCartographer, an automated proofsynthesis tool that combines supervised and reinforcement learning to more effectively explore the proof space. QEDCartographer incorporates the proofs' branching structure, enabling rewardfree search and overcoming the sparse reward problem inherent to formal verification. We evaluate QEDCartographer using the CoqGym benchmark of 68.5 K theorems from 124 open-source Coq projects. QEDCartographer fully automatically proves$\mathbf{2 1. 4 \%}$of the test-set theorems. Previous search-based proof-synthesis tools Tok, Tac, ASTactic, Passport, and Proverbot9001, which rely only on supervised learning, prove$9.6 \%, 9.8 \%, 10.9 \%$, 12.5 %, and 19.8 %, respectively. Diva, which combines 62 tools, proves 19.2 %. Comparing to the most effective prior tool, Proverbot9001, QEDCartographer produces 26 % shorter proofs 27 % faster, on average over the theorems both tools prove. Together, QEDCartographer and non-learning-based CoqHammer prove 31.8 % of the theorems, while CoqHammer alone proves$\mathbf{2 6. 6 \%}$. Our work demonstrates that reinforcement learning is a fruitful research direction for improving proof-synthesis tools' search mechanisms.

The Banana Bunchy Top Virus (BBTV) is one of the most economically important vector-borne banana diseases throughout the Asia-Pacific Basin and presents a significant challenge to the agricultural sector. Current models of BBTV are largely deterministic, limited by an incomplete understanding of interactions in complex natural systems, and the appropriate identification of parameters. A stochastic network-based Susceptible-Infected-Susceptible model has been created which simulates the spread of BBTV across the subsections of a banana plantation, parameterising nodal recovery, neighbouring and distant infectivity across summer and winter. Findings from posterior results achieved through Markov Chain Monte Carlo approach to approximate Bayesian computation suggest seasonality in all parameters, which are influenced by correlated changes in inspection accuracy, temperatures and aphid activity. This paper demonstrates how the model may be used for monitoring and forecasting of various disease management strategies to support policy-level decision making.