Model Predictive Control (MPC) represents nowadays one of the main methods employed for process control in industry. Its strong suits comprise a simple algorithm based on a straightforward formulation and the flexibility to deal with constraints. On the other hand it can be questioned its robustness regarding model uncertainties and external noises. Thus, a lot of efforts have been spent in the past years into the search of methods to address these shortcomings. In this paper we propose a robust MPC controller which stems from the idea of adding robustness in the prediction phase of the algorithm while leaving the core of MPC untouched. More precisely, we consider a robust Kalman filter that has been recently introduced and we further extend its usability to feedback control systems. Overall the proposed control algorithm allows to maintain all of the advantages of MPC with an additional improvement in performance and without any drawbacks in terms of computational complexity. To test the actual reliability of the algorithm we apply it to control a servomechanism system characterized by nonlinear dynamics.
Complex eukaryotic promoters normally contain multiple cis-regulatory sequences for different transcription factors (TFs). The binding patterns of the TFs to these sites, as well as the way the TFs interact with each other and with the RNA polymerase (RNAp), lead to combinatorial problems rarely understood in detail, especially under varying epigenetic conditions. The aim of this paper is to build a model describing how the main regulatory cluster of the olfactory receptor Or59b drives transcription of this gene in Drosophila. The cluster-driven expression of this gene is represented as the equilibrium probability of RNAp being bound to the promoter region, using a statistical thermodynamic approach. The RNAp equilibrium probability is computed in terms of the occupancy probabilities of the single TFs of the cluster to the corresponding binding sites, and of the interaction rules among TFs and RNAp, using experimental data of Or59b expression to tune the model parameters. The model reproduces correctly the changes in RNAp binding probability induced by various mutation of specific sites and epigenetic modifications. Some of its predictions have also been validated in novel experiments.
Motivation
The simultaneous availability of ATAC-seq and RNA-seq experiments allows to obtain a more in-depth knowledge on the regulatory mechanisms occurring in gene regulatory networks (GRNs). In this paper, we highlight and analyze two novel aspects that leverage on the possibility of pairing RNA-seq and ATAC-seq data. Namely we investigate the causality of the relationships between transcription factors (TFs), chromatin and target genes and the internal consistency between the two omics, here measured in terms of structural balance in the sample correlations along elementary length-3 cycles.
Results
We propose a framework that uses the a priori knowledge on the data to infer elementary causal regulatory motifs (namely chains and forks) in the network. It is based on the notions of conditional independence and partial correlation, and can be applied to both longitudinal and non-longitudinal data. Our analysis highlights a strong connection between the causal regulatory motifs that are selected by the data and the structural balance of the underlying sample correlation graphs: strikingly, > 97% of the selected regulatory motifs belong to a balanced subgraph. This result shows that internal consistency, as measured by structural balance, is close to a necessary condition for 3-node regulatory motifs to satisfy causality rules.
Supplementary information
Supplementary data are available at Bioinformatics online.
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