Perfect Sampling of the Master Equation for Gene Regulatory Networks

We present a Perfect Sampling algorithm that can be applied to the Master Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo methods and combines it with the Dominated Coupling From The Past (DCFTP) algorithm to provide guaranteed sampling from the stationary distribution. We show how the DCFTP-SSA can be generically applied to genetic networks with feedback formed by the interconnection of linear enzymatic reactions and nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the error and convergence of the DCFTP-SSA, as compared to the standard SSA, through a set of increasingly complex examples. Once the building blocks for GRNs have been introduced, the algorithm is applied to study properly averaged dynamic properties of two experimentally relevant genetic networks: the toggle switch, a two-dimensional bistable system, and the repressilator, a six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa

Finding role communities in directed networks using Role-Based Similarity, Markov Stability and the Relaxed Minimum Spanning Tree

We present a framework to cluster nodes in directed networks according to their roles by combining Role-Based Similarity (RBS) and Markov Stability, two techniques based on flows. First we compute the RBS matrix, which contains the pairwise similarities between nodes according to the scaled number of in- and out-directed paths of different lengths. The weighted RBS similarity matrix is then transformed into an undirected similarity network using the Relaxed Minimum-Spanning Tree (RMST) algorithm, which uses the geometric structure of the RBS matrix to unblur the network, such that edges between nodes with high, direct RBS are preserved. Finally, we partition the RMST similarity network into role-communities of nodes at all scales using Markov Stability to find a robust set of roles in the network. We showcase our framework through a biological and a man-made network.Comment: 4 pages, 2 figure

Robustness of Random Graphs Based on Natural Connectivity

Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the weighted number of closed walks of all lengths and can be regarded as the average eigenvalue obtained from the graph spectrum. In this article, we explore the natural connectivity of random graphs both analytically and numerically and show that it increases linearly with the average degree. By comparing with regular ring lattices and random regular graphs, we show that random graphs are more robust than random regular graphs; however, the relationship between random graphs and regular ring lattices depends on the average degree and graph size. We derive the critical graph size as a function of the average degree, which can be predicted by our analytical results. When the graph size is less than the critical value, random graphs are more robust than regular ring lattices, whereas regular ring lattices are more robust than random graphs when the graph size is greater than the critical value.Comment: 12 pages, 4 figure

Approximations of countably-infinite linear programs over bounded measure spaces

We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined weighted spaces of measures. We show how to approximate the optimal value, optimal points, and minimal points of these CILPs by solving finite-dimensional linear programs. The errors of our approximations converge to zero as the size of the finite-dimensional program approaches that of the original problem and are easy to bound in practice. We discuss the use of our methods in the computation of the stationary distributions, occupation measures, and exit distributions of Markov~chains

Dynamic Feature Engineering and model selection methods for temporal tabular datasets with regime changes

The application of deep learning algorithms to temporal panel datasets is difficult due to heavy non-stationarities which can lead to over-fitted models that under-perform under regime changes. In this work we propose a new machine learning pipeline for ranking predictions on temporal panel datasets which is robust under regime changes of data. Different machine-learning models, including Gradient Boosting Decision Trees (GBDTs) and Neural Networks with and without simple feature engineering are evaluated in the pipeline with different settings. We find that GBDT models with dropout display high performance, robustness and generalisability with relatively low complexity and reduced computational cost. We then show that online learning techniques can be used in post-prediction processing to enhance the results. In particular, dynamic feature neutralisation, an efficient procedure that requires no retraining of models and can be applied post-prediction to any machine learning model, improves robustness by reducing drawdown in regime changes. Furthermore, we demonstrate that the creation of model ensembles through dynamic model selection based on recent model performance leads to improved performance over baseline by improving the Sharpe and Calmar ratios of out-of-sample prediction performances. We also evaluate the robustness of our pipeline across different data splits and random seeds with good reproducibility of results

Feature Engineering Methods on Multivariate Time-Series Data for Financial Data Science Competitions

We apply different feature engineering methods for time-series to US market price data. The predictive power of models are tested against Numerai-Signals targets.Comment: arXiv admin note: substantial text overlap with arXiv:2303.0792