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

Barium sulfate precipitation as model reaction for segregation studies at pilot scale

The pptn. of barium sulfate from a basic EDTA complex upon addn. of a small vol. of acid in a stirred-tank reactor was used as a model reaction to study the local state of micromixing. Limitations and modifications of this reaction are presented, and its application on an industrial pilot scale is realized. A higher reaction rate is used in order to decrease the reaction time by using different concns. of reactants which modify the stability of the ppt. A study of this stability is presented. [on SciFinder (R)

Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-states sequences

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of `symbols', as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach - of a permutation procedure and a complexity analysis - is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach.Comment: 30 pages, 4 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

Atraumatic (pencil-point) versus conventional needles for lumbar puncture:a clinical practice guideline

Is the needle tip configuration important when performing a lumbar puncture for any indication? A systematic review published in the Lancet in December 2017 suggests that it is. The review found that using atraumatic (pencil-point) lumbar puncture needles instead of conventional lumbar puncture needles reduced the risk of post-dural-puncture headache and of return to hospital for additional pain control.1 This guideline recommendation aims to promptly and transparently translate this evidence to a clinical recommendation, following standards for GRADE methodology and trustworthy guidelines.2 The BMJ Rapid Recommendations panel makes a strong recommendation for the use of atraumatic needles for lumbar puncture in all patients regardless of age (adults and children) or indication instead of conventional needles.3 4 Box 1 shows the article and evidence linked to this Rapid Recommendation. The main infographic provides an overview of the absolute benefits and harms (although none were present here) of atraumatic needles. Table 1 below shows any evidence that has emerged since the publication of this guideline.publishedVersio