Gaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of $\mathcal{G}_n$, the set of all graphs in n vertices. One approach that has been proposed to tackle this problem is to limit search to subsets of $\mathcal{G}_n$. In this paper we study subsets that are vector subspaces with the cycle space $\mathcal{C}_n$ as the main example. We propose a novel prior on $\mathcal{C}_n$ based on linear combinations of cycle basis elements and present its theoretical properties. Using this prior, we implement a Markov chain Monte Carlo algorithm, and show that (i) posterior edge inclusion estimates computed with our technique are comparable to estimates from the standard technique despite searching a smaller graph space, and (ii) the vector space perspective enables straightforward implementation of MCMC algorithms.

Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous-time Markov processes. In this manuscript, the identifiability of the underlying network structure with a given stochastic system dynamics is studied. It is shown that some data types related to the associated stochastic dynamics can uniquely identify the underlying network structure as well as the system parameters. The accuracy of the presented network inference is investigated when given dynamical data are obtained via stochastic simulations.

A fundamental goal of systems biology is to create models that describe relationships between biological components. Networks are an increasingly popular approach to this problem. However, a scientist interested in modeling biological (e.g., gene expression) data as a network is quickly confounded by the fundamental problem: how to construct the network? It is fairly easy to construct a network, but is it the network for the problem being considered? This is an important problem with three fundamental issues: How to weight edges in the network in order to capture actual biological interactions? What is the effect of the type of biological experiment used to collect the data from which the network is constructed? How to prune the weighted edges (or what cut-off to apply)? Differences in the construction of networks could lead to different biological interpretations.

Indeed, we find that there are statistically significant dissimilarities in the functional content and topology between gene co-expression networks constructed using different edge weighting methods, data types, and edge cut-offs. We show that different types of known interactions, such as those found through Affinity Capture-Luminescence or Synthetic Lethality experiments, appear in significantly varying amounts in networks constructed in different ways. Hence, we demonstrate that different biological questions may be answered by the different networks. Consequently, we posit that the approach taken to build a network can be matched to biological questions to get targeted answers. More study is required to understand the implications of different network inference approaches and to draw reliable conclusions from networks used in the field of systems biology.