Graphical Conditions for the Existence, Unicity and Number of Regular Models

The regular models of a normal logic program are a particular type of partial (i.e. 3-valued) models which correspond to stable partial models with minimal undefinedness. In this paper, we explore graphical conditions on the dependency graph of a finite ground normal logic program to analyze the existence, unicity and number of regular models for the program. We show three main results: 1) a necessary condition for the existence of non-trivial (i.e. non-2-valued) regular models, 2) a sufficient condition for the unicity of regular models, and 3) two upper bounds for the number of regular models based on positive feedback vertex sets. The first two conditions generalize the finite cases of the two existing results obtained by You and Yuan (1994) for normal logic programs with well-founded stratification. The third result is also new to the best of our knowledge. Key to our proofs is a connection that we establish between finite ground normal logic programs and Boolean network theory.

Reactmine: a search algorithm for inferring chemical reaction networks from time series data

Inferring chemical reaction networks (CRN) from time series data is a challenge encouraged by the growing availability of quantitative temporal data at the cellular level. This motivates the design of algorithms to infer the preponderant reactions between the molecular species observed in a given biochemical process, and help to build CRN model structure and kinetics. Existing ODE-based inference methods such as SINDy resort to least square regression combined with sparsity-enforcing penalization, such as Lasso. However, when the input time series are only available in wild type conditions in which all reactions are present, we observe that current methods fail to learn sparse models. Results: We present Reactmine, a CRN learning algorithm which enforces sparsity by inferring reactions in a sequential fashion within a search tree of bounded depth, ranking the inferred reaction candidates according to the variance of their kinetics, and re-optimizing the CRN kinetic parameters on the whole trace in a final pass to rank the inferred CRN candidates. We first evaluate its performance on simulation data from a benchmark of hidden CRNs, together with algorithmic hyperparameter sensitivity analyses, and then on two sets of real experimental data: one from protein fluorescence videomicroscopy of cell cycle and circadian clock markers, and one from biomedical measurements of systemic circadian biomarkers possibly acting on clock gene expression in peripheral organs. We show that Reactmine succeeds both on simulation data by retrieving hidden CRNs where SINDy fails, and on the two real datasets by inferring reactions in agreement with previous studies.