Cleaning large correlation matrices: tools from random matrix theory

This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.Comment: 165 pages, article submitted to Physics Report

Instanton Approach to Large NN Harish-Chandra-Itzykson-Zuber Integrals

We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.Comment: 5 pages, 1 figur

A disassembly-driven mechanism explains F-actin-mediated chromosome transport in starfish oocytes.

While contraction of sarcomeric actomyosin assemblies is well understood, this is not the case for disordered networks of actin filaments (F-actin) driving diverse essential processes in animal cells. For example, at the onset of meiosis in starfish oocytes a contractile F-actin network forms in the nuclear region transporting embedded chromosomes to the assembling microtubule spindle. Here, we addressed the mechanism driving contraction of this 3D disordered F-actin network by comparing quantitative observations to computational models. We analyzed 3D chromosome trajectories and imaged filament dynamics to monitor network behavior under various physical and chemical perturbations. We found no evidence of myosin activity driving network contractility. Instead, our observations are well explained by models based on a disassembly-driven contractile mechanism. We reconstitute this disassembly-based contractile system in silico revealing a simple architecture that robustly drives chromosome transport to prevent aneuploidy in the large oocyte, a prerequisite for normal embryonic development

Accuracy Assessment of the ESA CCI 20M Land Cover Map: Kenya, Gabon, Ivory Coast and South Africa

This working paper presents the overall and spatial accuracy assessment of the European Space Agency (ESA) 20 m prototype land cover map for Africa for four countries: Kenya, Gabon, Ivory Coast and South Africa. This accuracy assessment was undertaken as part of the ESA-funded CrowdVal project. The results varied from 44% (for South Africa) to 91% (for Gabon). In the case of Kenya (56% overall accuracy) and South Africa, these values are largely caused by the confusion between grassland and shrubland. However, if a weighted confusion matrix is used, which diminishes the importance of the confusion between grassland and shrubs, the overall accuracy for Kenya increases to 79% and for South Africa, 75%. The overall accuracy for Ivory Coast (47%) is a result of a highly fragmented land cover, which makes it a difficult country to map with remote sensing. The exception was Gabon with a high overall accuracy of 91%, but this can be explained by the high amount of tree cover across the country, which is a relatively easy class to map

Brisure de symétrie et Polarisation cellulaire imposée par un signal mécanique externe

Cell polarity establishment implies a symmetry-breaking event, resulting in an axis along which the cell reorganizes. Whether the initial event that triggers polarity arises spontaneously or requires an external cue remains controversial. We set up a dual-objective system that combines quantitative mechanical manipulation using optical tweezers and fluorescence three-dimensional imaging to monitor in real time the local and global cell response to the application of a single fibronectin-coated trapped bead, mimicking an adhesion site of weak rigidity. Here we show that single and weak mechanical cue applied on detached round fibroblasts is required to control the location and duration of symmetry breaking of cortical actomyosin gel instability. Furthermore, we demonstrate that cells respond at a macroscopic level since the induced asymmetric actomyosin flow triggers the 3D migratory polarization axis and determines its orientation. As an initial event, the microtubule-independent actomyosin flow polarizes towards the opposite pole of the cue and drives higher contractility at the rear of the cell that persists after the application of mechanical stress has been halted. Microtubules are further required for long-term growth of leading edge protrusion associated with the MTOC reorientation relative to the cue. These findings support a model whereby the stochastic and transient symmetry-breaking events occuring in detached oscillating cells are not able to drive cell polarity establishment, the mechanical stress being required to trigger processes of global auto organization necessary for long-term functional polarization.L'établissement de la polarité cellulaire implique une brisure de symétrie, résultant en la formation d'un axe suivant lequel la cellule s'organise.Que l'évènement initial déclencheur de la mise en place de la polarité cellulaire soit spontané ou nécessite un signal externe reste controversé. Nous avons mis en place un système à double objectif, consistant en un outil de micromanipulation par pinces optiques couplé à l'imagerie en fluorescence pour suivre en temps réel la réponse locale et globale des cellules à l'application d'une bille fonctionnalisée à la fibronectine, mimant ainsi un site d'adhésion de faible rigidité. Nous montrons que l'application de points de tension mécanique de faible rigidité est nécessaire pour contrôler la position et la durée de la brisure de symétrie du gel d'actomyosine; En outre, nous démontrons également que le flux asymétrique d'actomyosine induit par le point de tension déclenche et sous-tend la formation et l'orientation d'un axe de migration polarisée en trois dimensions. Initialement, le flux se polarise dans la direction opposée à la position de la bille, ce qui renforce l'activité contractile à un pôle de la cellule, et cela se poursuit après que la bille se soit échappée du piège optique. Les microtubules interviennent dans un second temps pour participer à la croissance d'une protrusion sous la bille, et à la réorientation du centrosome dans la direction de la bille. Ces résultats suggèrent un modèle dans lequel la brisure de symétrique doit être stabilisée par des contraintes mécaniques afin de déclencher un processus d'auto-organisation globale, conduisant à l'établissement et au maintien d'un nouvel axe de polarité.PARIS7-Bibliothèque centrale (751132105) / SudocSudocFranceF

A disassembly-driven mechanism explains F-actin-mediated chromosome transport in starfish oocytes.

While contraction of sarcomeric actomyosin assemblies is well understood, this is not the case for disordered networks of actin filaments (F-actin) driving diverse essential processes in animal cells. For example, at the onset of meiosis in starfish oocytes a contractile F-actin network forms in the nuclear region transporting embedded chromosomes to the assembling microtubule spindle. Here, we addressed the mechanism driving contraction of this 3D disordered F-actin network by comparing quantitative observations to computational models. We analyzed 3D chromosome trajectories and imaged filament dynamics to monitor network behavior under various physical and chemical perturbations. We found no evidence of myosin activity driving network contractility. Instead, our observations are well explained by models based on a disassembly-driven contractile mechanism. We reconstitute this disassembly-based contractile system in silico revealing a simple architecture that robustly drives chromosome transport to prevent aneuploidy in the large oocyte, a prerequisite for normal embryonic development

Breaking the Dynamic Instability of the Actomyosin Cortex Triggered by a Single Mechanical Cue Drives Cell Polarity in Non-Adherent Cells

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