Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

Beyond forcing scenarios: predicting climate change through response operators in a coupled general circulation model

Global Climate Models are key tools for predicting the future response of the climate system to a variety of natural and anthropogenic forcings. Here we show how to use statistical mechanics to construct operators able to flexibly predict climate change for a variety of climatic variables of interest. We perform our study on a fully coupled model - MPI-ESM v.1.2 - and for the first time we prove the effectiveness of response theory in predicting future climate response to CO2 increase on a vast range of temporal scales, from inter-annual to centennial, and for very diverse climatic quantities. We investigate within a unified perspective the transient climate response and the equilibrium climate sensitivity and assess the role of fast and slow processes. The prediction of the ocean heat uptake highlights the very slow relaxation to a newly established steady state. The change in the Atlantic Meridional Overturning Circulation (AMOC) and of the Antarctic Circumpolar Current (ACC) is accurately predicted. The AMOC strength is initially reduced and then undergoes a slow and only partial recovery. The ACC strength initially increases as a result of changes in the wind stress, then undergoes a slowdown, followed by a recovery leading to a overshoot with respect to the initial value. Finally, we are able to predict accurately the temperature change in the Northern Atlantic

First Dating of a Recombination Event in Mammalian Tick-Borne Flaviviruses

The mammalian tick-borne flavivirus group (MTBFG) contains viruses associated with important human and animal diseases such as encephalitis and hemorrhagic fever. In contrast to mosquito-borne flaviviruses where recombination events are frequent, the evolutionary dynamic within the MTBFG was believed to be essentially clonal. This assumption was challenged with the recent report of several homologous recombinations within the Tick-borne encephalitis virus (TBEV). We performed a thorough analysis of publicly available genomes in this group and found no compelling evidence for the previously identified recombinations. However, our results show for the first time that demonstrable recombination (i.e., with large statistical support and strong phylogenetic evidences) has occurred in the MTBFG, more specifically within the Louping ill virus lineage. Putative parents, recombinant strains and breakpoints were further tested for statistical significance using phylogenetic methods. We investigated the time of divergence between the recombinant and parental strains in a Bayesian framework. The recombination was estimated to have occurred during a window of 282 to 76 years before the present. By unravelling the temporal setting of the event, we adduce hypotheses about the ecological conditions that could account for the observed recombination

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises

Micro-connectomics: probing the organization of neuronal networks at the cellular scale.

Defining the organizational principles of neuronal networks at the cellular scale, or micro-connectomics, is a key challenge of modern neuroscience. In this Review, we focus on graph theoretical parameters of micro-connectome topology, often informed by economical principles that conceptually originated with Ramón y Cajal's conservation laws. First, we summarize results from studies in intact small organisms and in samples from larger nervous systems. We then evaluate the evidence for an economical trade-off between biological cost and functional value in the organization of neuronal networks. Various results suggest that many aspects of neuronal network organization are indeed the outcome of competition between these two fundamental selection pressures.This work was supported by the National Institute of Health Research (NIHR) Cambridge Biomedical Research Centre.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the Nature Publishing Group

Introduction to the special issue on the statistical mechanics of climate

We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions