Non–Parametric Estimation of Mutual Information through the Entropy of the Linkage

A new, non–parametric and binless estimator for the mutual information of a d–dimensional random vector is proposed. First of all, an equation that links the mutual information to the entropy of a suitable random vector with uniformly distributed components is deduced. When d = 2 this equation reduces to the well known connection between mutual information and entropy of the copula function associated to the original random variables. Hence, the problem of estimating the mutual information of the original random vector is reduced to the estimation of the entropy of a random vector obtained through a multidimensional transformation. The estimator we propose is a two–step method: first estimate the transformation and obtain the transformed sample, then estimate its entropy. The properties of the new estimator are discussed through simulation examples and its performances are compared to those of the best estimators in the literature. The precision of the estimator converges to values of the same order of magnitude of the best estimator tested. However, the new estimator is unbiased even for larger dimensions and smaller sample sizes, while the other tested estimators show a bias in these cases

A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena, such as a deficiency and a bistability. It is advocated that the diffusion approximation can be considered as an alternative theoretical approach to study the reaction networks rather than a simulation shortcut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of reaction networks that the deterministic model misses. We provide an explicit construction of the original process and the diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potential directions of the developments

CONNECTOR, fitting and clustering of longitudinal data to reveal a new risk stratification system

Motivation: The transition from evaluating a single time point to examining the entire dynamic evolution of a system is possible only in the presence of the proper framework. The strong variability of dynamic evolution makes the definition of an explanatory procedure for data fitting and clustering challenging. Results: We developed CONNECTOR, a data-driven framework able to analyze and inspect longitudinal data in a straightforward and revealing way. When used to analyze tumor growth kinetics over time in 1599 patient-derived xenograft growth curves from ovarian and colorectal cancers, CONNECTOR allowed the aggregation of time-series data through an unsupervised approach in informative clusters. We give a new perspective of mechanism interpretation, specifically, we define novel model aggregations and we identify unanticipated molecular associations with response to clinically approved therapies. Availability and implementation: CONNECTOR is freely available under GNU GPL license at https://qbioturin.github.io/connector and https://doi.org/10.17504/protocols.io.8epv56e74g1b/v1