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

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

The little skate genome and the evolutionary emergence of wing-like fins

Skates are cartilaginous fish whose body plan features enlarged wing-like pectoral fins, enabling them to thrive in benthic environments1,2. However, the molecular underpinnings of this unique trait remain unclear. Here we investigate the origin of this phenotypic innovation by developing the little skate Leucoraja erinacea as a genomically enabled model. Analysis of a high-quality chromosome-scale genome sequence for the little skate shows that it preserves many ancestral jawed vertebrate features compared with other sequenced genomes, including numerous ancient microchromosomes. Combining genome comparisons with extensive regulatory datasets in developing fins—including gene expression, chromatin occupancy and three-dimensional conformation—we find skate-specific genomic rearrangements that alter the three-dimensional regulatory landscape of genes that are involved in the planar cell polarity pathway. Functional inhibition of planar cell polarity signalling resulted in a reduction in anterior fin size, confirming that this pathway is a major contributor to batoid fin morphology. We also identified a fin-specific enhancer that interacts with several hoxa genes, consistent with the redeployment of hox gene expression in anterior pectoral fins, and confirmed its potential to activate transcription in the anterior fin using zebrafish reporter assays. Our findings underscore the central role of genome reorganization and regulatory variation in the evolution of phenotypes, shedding light on the molecular origin of an enigmatic trait

InterGEO: a digital platform for university education on geomorphological heritage

The project InterGEO was carried out with the objective to disseminate knowledge on geomorphological heritage by developing a digital learning platform. It aims at improving students' autonomy by the reduction of face-to-face teaching and increasing autonomous learning as well as promoting international interactions between students interested in geomorphological heritage. A completely free-access virtual course on geomorphosites was developed with the Learning Management System Moodle. The course is divided into 24 thematic chapters, each of them containing a short description, a list of references and selected publications, as well as other educational material (videos, virtual fieldtrips, etc.). In particular, several videos allow presenting in a dynamic way concepts and examples. The paper presents the tool and its use in academic programmes in six European universities, where it was tested, in various contexts (Bachelors' and Masters' programmes; students in geography or geology; general courses in geomorphology and specific courses on geoheritage and geoconservation), before discussing the advantages and challenges the tool is facing. The InterGEO platform is an easy-to-use and friendly educational tool, which allows developing blended learning activities; it is flexible and adaptable in various learning contexts.The coordination tasks (appointment of an assistant) and two workshops in Lausanne were financed by the University of Lausanne (Teaching Innovation Fund and Investment Fund of the Faculty of Geosciences and Environment, FGSE). The videos were designed and created with support of the universities of Lausanne (TIF) and Savoie Mont Blanc (IDEFI Promising and ReflexPro; LabEx ITEM)

Effects of Ionomycin on Egg Activation and Early Development in Starfish

Ionomycin is a Ca2+-selective ionophore that is widely used to increase intracellular Ca2+ levels in cell biology laboratories. It is also occasionally used to activate eggs in the clinics practicing in vitro fertilization. However, neither the precise molecular action of ionomycin nor its secondary effects on the eggs' structure and function is well known. In this communication we have studied the effects of ionomycin on starfish oocytes and zygotes. By use of confocal microscopy, calcium imaging, as well as light and transmission electron microscopy, we have demonstrated that immature oocytes exposed to ionomycin instantly increase intracellular Ca2+ levels and undergo structural changes in the cortex. Surprisingly, when microinjected into the cells, ionomycin produced no Ca2+ increase. The ionomycin-induced Ca2+ rise was followed by fast alteration of the actin cytoskeleton displaying conspicuous depolymerization at the oocyte surface and in microvilli with concomitant polymerization in the cytoplasm. In addition, cortical granules were disrupted or fused with white vesicles few minutes after the addition of ionomycin. These structural changes prevented cortical maturation of the eggs despite the normal progression of nuclear envelope breakdown. At fertilization, the ionomycin-pretreated eggs displayed reduced Ca2+ response, no elevation of the fertilization envelope, and the lack of orderly centripetal translocation of actin fibers. These alterations led to difficulties in cell cleavage in the monospermic zygotes and eventually to a higher rate of abnormal development. In conclusion, ionomycin has various deleterious impacts on egg activation and the subsequent embryonic development in starfish. Although direct comparison is difficult to make between our findings and the use of the ionophore in the in vitro fertilization clinics, our results call for more defining investigations on the issue of a potential risk in artificial egg activation

The little skate genome and the evolutionary emergence of wing-like fin appendages

Skates are cartilaginous fish whose novel body plan features remarkably enlarged wing-like pectoral fins that allow them to thrive in benthic environments. The molecular underpinnings of this unique trait, however, remain elusive. Here we investigate the origin of this phenotypic innovation by developing the little skate Leucoraja erinacea as a genomically enabled model. Analysis of a high-quality chromosome-scale genome sequence for the little skate shows that it preserves many ancestral jawed vertebrate features compared with other sequenced genomes, including numerous ancient microchromosomes. Combining genome comparisons with extensive regulatory datasets in developing fins (gene expression, chromatin occupancy and three-dimensional (3D) conformation) we find skate-specific genomic rearrangements that alter the 3D regulatory landscape of genes involved in the planar cell polarity (PCP) pathway. Functional inhibition of PCP signaling resulted in marked reduction of anterior fin size, confirming this pathway as a major contributor of batoid fin morphology. We also identified a fin-specific enhancer that interacts with 3' HOX genes, consistent with the redeployment of Hox gene expression in anterior pectoral fins, and confirmed the potential of this element to activate transcription in the anterior fin using zebrafish reporter assays. Our findings underscore the central role of genome reorganizations and regulatory variation in the evolution of phenotypes, shedding light on the molecular origin of an enigmatic trait