Simon Dobson’s research while affiliated with University of St Andrews and other places

The solubility of chemical substances in water is a critical parameter in pharmaceutical development, environmental chemistry, agrochemistry, and other fields; however, accurately predicting it remains a challenge. This study aims to evaluate and compare the effectiveness of some of the most popular machine learning modeling methods and molecular featurization techniques in predicting aqueous solubility. Although these methods were not implemented in a competitive environment, some of their performance surpassed previous benchmarks, offering gradual but significant improvements. Our results show that methods based on graph convolution and graph attention mechanisms demonstrated exceptional predictive abilities with high-quality data sets, albeit with a sensitivity to data noise and errors. In contrast, models leveraging molecular descriptors not only provided better interpretability but also showed more resilience when dealing with inherent noise and errors in data. Our analysis of over 4000 molecular descriptors used in various models identified that approximately 800 of these descriptors make a significant contribution to solubility prediction. These insights offer guidance and direction for future developments in solubility prediction.

The solubility of a chemical in water is a critical parameter in drug development and other fields such as environmental chemistry and agrochemistry, but its in silico prediction presents a formidable challenge. Here, we apply a suite of graph-based machine learning algorithms to the benchmark problems posed over several years in international ``solubility challenges'', and also to our own newly-compiled dataset of over 11,000 compounds. We find that graph convolutional networks (GCNs) and graph attention networks (GATs) both show excellent predictive power against these datasets. Although not executed under competition conditions, these approaches achieve better scores in several instances than the best models available at the time. They offer an incremental, but still significant, improvement when compared against a range of existing cheminformatics approaches.

It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik et al., Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif-based theory would be superior to a tree one, since additional neighbor correlations are encapsulated in the motif structure. In this paper, we examine bond percolation on random and real world networks using belief propagation in conjunction with edge-disjoint motif covers. We derive exact message passing expressions for cliques and chordless cycles of finite size. Our theoretical model gives good agreement with Monte Carlo simulation and offers a simple, yet substantial improvement on traditional message passing, showing that this approach is suitable to study the properties of random and empirical networks.

In this paper we introduce a novel description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows us to find the expected size of the giant connected component (GCC) of two sequential bond percolation processes in which the bond occupancy probability of the second process is modulated (increased or decreased) by a node being inside or outside of the GCC created by the first process. In the context of epidemic spreading this amounts to both a antagonistic partial immunity or a synergistic partial coinfection interaction between the two sequential diseases. We examine configuration model networks with tunable clustering. We find that the emergent evolutionary behaviour of the second strain is highly dependent on the details of the coupling between the strains. Contact clustering generally reduces the outbreak size of the second strain relative to unclustered topologies; however, positive assortativity induced by clustered contacts inverts this conclusion for highly transmissible disease dynamics.

It is well known that tree-based theories can describe the properties of undirected clustered networks with extremely accurate results [S. Melnik, \textit{et al}. Phys. Rev. E 83, 036112 (2011)]. It is reasonable to suggest that a motif based theory would be superior to a tree one; since additional neighbour correlations are encapsulated in the motif structure. In this paper we examine bond percolation on random and real world networks using belief propagation in conjunction with edge-disjoint motif covers. We derive exact message passing expressions for cliques and chordless cycles of finite size. Our theoretical model gives good agreement with Monte Carlo simulation and offers a simple, yet substantial improvement on traditional message passing showing that this approach is suitable to study the properties of random and empirical networks.

In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our analytical method is based on generating functions. We also propose a Monte Carlo graph generation algorithm to draw random networks from the ensemble of graphs with fixed statistics. We use our model to understand the effect that network microstructure has, through the arrangement of clustering, on the global properties. Finally, we use an edge disjoint clique cover to represent empirical networks using our formulation, finding the resultant model offers a significant improvement over edge-based theory.

In this paper we examine the emergent structures of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process, in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations, and a collaborative branching process, where percolation is performed on the giant connected component (GCC) instead. We investigate the behavior of these models, including the expected size of the GCC for a given generation, the critical percolation probability, and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erdős-Renyi and scale-free random graphs. This model can be interpreted as a seasonal N-strain model of disease spreading.

Correlations among the degrees of vertices in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for vertices in the giant component of clustered configuration model networks which are composed of clique subgraphs. We use this model to investigate, in detail, the organization among nearest-neighbor subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbor in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.