Case-Analysis for Rippling and Inductive Proof

Rippling is a heuristic used to guide rewriting and is typically used for inductive theorem proving. We introduce a method to support case-analysis within rippling. Like earlier work, this allows goals containing if-statements to be proved automatically. The new contribution is that our method also supports case-analysis on datatypes. By locating the case-analysis as a step within rippling we also maintain the termination. The work has been implemented in IsaPlanner and used to extend the existing inductive proof method. We evaluate this extended prover on a large set of examples from Isabelle’s theory library and from the inductive theorem proving literature. We find that this leads to a significant improvement in the coverage of inductive theorem proving. The main limitations of the extended prover are identified, highlight the need for advances in the treatment of assumptions during rippling and when conjecturing lemmas

Assessment of regression methods for inference of regulatory networks involved in circadian regulation

We assess the accuracy of three established regression methods for reconstructing gene and protein regulatory networks in the context of circadian regulation. Data are simulated from a recently published regulatory network of the circadian clock in Arabidopsis thaliana, in which protein and gene interactions are described by a Markov jump process based on Michaelis-Menten kinetics. We closely follow recent experimental protocols, including the entrainment of seedlings to different light-dark cycles and the knock-out of various key regulatory genes. Our study provides relative assessment scores for the comparison of state-of-the art regression methods, investigates the influence of systematically missing values related to unknown protein concentrations and mRNA transcription rates, and quantifies the dependence of the performance on the degree of recurrency

Reconstructing ecological networks with hierarchical Bayesian regression and Mondrian processes

Ecological systems consist of complex sets of interactions among species and their environment, the understanding of which has implications for predicting environmental response to perturbations such as invading species and climate change. However, the revelation of these interactions is not straightforward, nor are the interactions necessarily stable across space. Machine learning can enable the recovery of such complex, spatially varying interactions from relatively easily obtained species abundance data. Here, we describe a novel Bayesian regression and Mondrian process model (BRAMP) for reconstructing species interaction networks from observed field data. BRAMP enables robust inference of species interactions considering autocorrelation in species abundances and allowing for variation in the interactions across space. We evaluate the model on spatially explicit simulated data, produced using a trophic niche model combined with stochastic population dynamics. We compare the model’s performance against L1-penalized sparse regression (LASSO) and non-linear Bayesian networks with the BDe scoring scheme. Finally, we apply BRAMP to real ecological data