Karhunen-Lo`eve Decomposition of Extensive Chaos

We show that the number of KLD (Karhunen-Lo`eve decomposition) modes D_KLD(f) needed to capture a fraction f of the total variance of an extensively chaotic state scales extensively with subsystem volume V. This allows a correlation length xi_KLD(f) to be defined that is easily calculated from spatially localized data. We show that xi_KLD(f) has a parametric dependence similar to that of the dimension correlation length and demonstrate that this length can be used to characterize high-dimensional inhomogeneous spatiotemporal chaos.Comment: 12 pages including 4 figures, uses REVTeX macros. To appear in Phys. Rev. Let

Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices

We present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is quite general and applies to other related problems, e.g. the joint large deviation function for large fluctuations of top eigenvalues. Our results are relevant to widely employed data compression techniques, namely the principal components analysis. Analytical predictions are verified by extensive numerical simulations.Comment: 4 pages, 3 .eps figures include

Wishart and Anti-Wishart random matrices

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^\dagger A$, for any finite number of rows and columns of $A$, without any large N approximations. In particular we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure of reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.Comment: 11 pages; v2: references updated + some clarifications added; v3: version to appear in J. Phys. A, Special Issue on Random Matrix Theor

Statistics of Atmospheric Correlations

For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show that the random matrix approach can be beneficially applied to a completely different classical domain, namely, to the empirical correlation matrices obtained from the analysis of the basic atmospheric parameters that characterise the state of atmosphere. We show that the spectrum of atmospheric correlation matrices satisfy the random matrix prescription. In particular, the eigenmodes of the atmospheric empirical correlation matrices that have physical significance are marked by deviations from the eigenvector distribution.Comment: 8 pages, 9 figs, revtex; To appear in Phys. Rev.

Southward re-distribution of tropical tuna fisheries activity can be explained by technological and management change

There is broad evidence of climate change causing shifts in fish distribution worldwide, but less is known about the response of fisheries to these changes. Responses to climate-driven shifts in a fishery may be constrained by existing management or institutional arrangements and technological settings. In order to understand how fisheries are responding to ocean warming, we investigate purse seine fleets targeting tropical tunas in the east Atlantic Ocean using effort and sea surface temperature anomaly (SSTA) data from 1991 to 2017. An analysis of the spatial change in effort using a centre of gravity approach and empirical orthogonal functions is used to assess the spatiotemporal changes in effort anomalies and investigate links to SSTA. Both analyses indicate that effort shifts southward from the equator, while no clear pattern is seen northward from the equator. Random forest models show that while technology and institutional settings better explain total effort, SSTA is playing a role when explaining the spatiotemporal changes of effort, together with management and international agreements. These results show the potential of management to minimize the impacts of climate change on fisheries activity. Our results provide guidance for improved understanding about how climate, management and governance interact in tropical tuna fisheries, with methods that are replicable and transferable. Future actions should take into account all these elements in order to plan successful adaptation. © 2020 The Authors. Fish and Fisheries published by John Wiley & Sons Ltd.This research is supported by the project CLOCK, under the European Horizon 2020 Program, ERC Starting Grant Agreement nº679812 funded by the European Research Council. It is also supported by the Basque Government through the BERC 2018-2021 programme and by the Spanish Ministry of Economy and Competitiveness MINECO through the BC3 María de Maeztu excellence accreditation MDM- 2017-0714. We thank, without implicating, C. Palma for his helpful advice on the ICCAT database and M. Gabantxo and H. Gabantxo for their knowledge transfer about tropical tuna fisheries. Also, we thank I. Arostegui for her comments during the design of the random forest; F. Saborido, A. Tidd and H. Arrizabalaga for scientific advice and H. Murua and M. Ortiz for providing ICCAT data. Elena Ojea thanks the Xunta the Galicia GAIN Oportunius programme and Consellería de Educación (Galicia, Spain) for additional financial support

Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value =N/c decreases for large N as $\sim \exp[-\frac{\beta}{2}N^2 \Phi_{-}(\frac{2}{\sqrt{c}}+1;c)]$, where \beta=1,2 correspond respectively to real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large deviation function that we compute explicitly. The result for the Anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of constrained Wishart matrices whose eigenvalues are forced to be smaller than a fixed barrier. The numerical simulations are in excellent agreement with the analytical predictions.Comment: Published version. References and appendix adde