Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Characterizing genomic alterations in cancer by complementary functional associations.

Systematic efforts to sequence the cancer genome have identified large numbers of mutations and copy number alterations in human cancers. However, elucidating the functional consequences of these variants, and their interactions to drive or maintain oncogenic states, remains a challenge in cancer research. We developed REVEALER, a computational method that identifies combinations of mutually exclusive genomic alterations correlated with functional phenotypes, such as the activation or gene dependency of oncogenic pathways or sensitivity to a drug treatment. We used REVEALER to uncover complementary genomic alterations associated with the transcriptional activation of β-catenin and NRF2, MEK-inhibitor sensitivity, and KRAS dependency. REVEALER successfully identified both known and new associations, demonstrating the power of combining functional profiles with extensive characterization of genomic alterations in cancer genomes

Human skeletal muscle plasmalemma alters its structure to change its Ca2+-handling following heavy-load resistance exercise

High-force eccentric exercise results in sustained increases in cytoplasmic Ca2+ levels ([Ca2+]cyto), which can cause damage to the muscle. Here we report that a heavy-load strength training bout greatly alters the structure of the membrane network inside the fibres, the tubular (t-) system, causing the loss of its predominantly transverse organization and an increase in vacuolation of its longitudinal tubules across adjacent sarcomeres. The transverse tubules and vacuoles displayed distinct Ca2+-handling properties. Both t-system components could take up Ca2+ from the cytoplasm but only transverse tubules supported store-operated Ca2+ entry. The retention of significant amounts of Ca2+ within vacuoles provides an effective mechanism to reduce the total content of Ca2+ within the fibre cytoplasm. We propose this ability can reduce or limit resistance exercise-induced, Ca2+-dependent damage to the fibre by the reduction of [Ca2+]cyto to help maintain fibre viability during the period associated with delayed onset muscle soreness