The recurrence time of Dansgaard-Oeschger events and limits on the possible periodic component

By comparing the high-resolution isotopic records from the GRIP and NGRIP icecores, we approximately separate the climate signal from local noise to obtain an objective criterion for defining Dansgaard-Oeschger events. Our analysis identifies several additional short lasting events, increasing the total number of DO events to 27 in the period 12-90 kyr BP. The quasi-regular occurrence of the DO events could indicate a stochastic or coherent resonance mechanism governing their origin. From the distribution of waiting times we obtain a statistical upper bound on the strength of a possible periodic forcing. This finding indicates that the climate shifts are purely noise driven with no underlying periodicity.Comment: 9 figure

Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model

We study the stochastic FitzHugh-Nagumo equations, modelling the dynamics of neuronal action potentials, in parameter regimes characterised by mixed-mode oscillations. The interspike time interval is related to the random number of small-amplitude oscillations separating consecutive spikes. We prove that this number has an asymptotically geometric distribution, whose parameter is related to the principal eigenvalue of a substochastic Markov chain. We provide rigorous bounds on this eigenvalue in the small-noise regime, and derive an approximation of its dependence on the system's parameters for a large range of noise intensities. This yields a precise description of the probability distribution of observed mixed-mode patterns and interspike intervals.Comment: 36 page

Two modes of glacial climate during the late stage 5 identified in Greenland ice core records

International audienceFrom a detailed analysis of marine and terrestrial aerosol tracers in the NGRIP ice core we identified two distinct glacial atmospheric flow patterns. The climate transition from Marine Isotope Stage 5 (MIS 5) to MIS 4, at approximately 75 kyr BP, marks a shift between two different atmospheric flow regimes. Before this transition, during MIS 5d-a, the state of atmospheric flow was alternating between the two modes of different flow patterns, while a more persistent flow pattern was prevailing through the glacial period afterwards. These changes are accompanied by strong changes in an independent Greenland ice core proxy, namely the deuterium excess from the GRIP ice core, reflecting changes in the hydrological cycle and moisture source temperatures as well. The changes in atmospheric flow pattern are correlated with changed extent of ice-rafted detritus (IRD) deposition in the North Atlantic, indicating that the state of the atmospheric flow was highly sensitive to the waxing and waning of the Laurentide ice sheet

DYNAMIC BEHAVIOR ANALYSIS OF THE GLOMERULO-TUBULAR BALANCE MEDIATED BY THE EFFERENT BLOOD VISCOSITY

International audienceA mathematical model of the dynamics of a single nephron function relating glomerulo-tubular balance, tubule-glomerular feedback, and peritubular blood viscosity is developed. Based upon experimental data, the model shows that complex behaviors of the nephron can be modulated by changes in the efferent arteriole blood viscosity. The main hypothesis is that the reabsorbed mass flow is modulated by the hematocrit of the efferent arteriole, in addition to the Starling forces. From a mathematical perspective, these behaviors can be explained by a bifurcation diagram analysis where the efferent blood viscosity is taken as the bifurcation parameter. This analytical description allows to predict changes in proximal convoluted tubule reabsorption, following changes in peritubular capillary viscosity generated by periodic changes in the glomerular filtration rate. Thus, the model links the tubule-glomerular feedback with the glomerular tubular balance

On the state dependency of fast feedback processes in (palaeo) climate sensitivity

Palaeo data have been frequently used to determine the equilibrium (Charney) climate sensitivity $S^a$, and - if slow feedback processes (e.g. land ice-albedo) are adequately taken into account - they indicate a similar range as estimates based on instrumental data and climate model results. Most studies implicitly assume the (fast) feedback processes to be independent of the background climate state, e.g., equally strong during warm and cold periods. Here we assess the dependency of the fast feedback processes on the background climate state using data of the last 800 kyr and a conceptual climate model for interpretation. Applying a new method to account for background state dependency, we find $S^a=0.61\pm0.06$ K(Wm$^{-2}$)$^{-1}$ using the latest LGM temperature reconstruction and significantly lower climate sensitivity during glacial climates. Due to uncertainties in reconstructing the LGM temperature anomaly, $S^a$ is estimated in the range $S^a=0.55-0.95$ K(Wm$^{-2}$)$^{-1}$.Comment: submitted to Geophysical Research Letter

Levy flights and Levy -Schroedinger semigroups

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.Comment: To appear in Cent. Eur. J. Phys. (2010

Bayesian Network Enhanced with Structural Reliability Methods: Methodology

We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced Bayesian network (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence structures, as present in infrastructure and structural systems, and they facilitate Bayesian updating of the model when new information becomes available. On the other hand, SRMs enable accurate assessment of probabilities of rare events represented by computationally demanding, physically-based models. By combining the two methods, the eBN framework provides a unified and powerful tool for efficiently computing probabilities of rare events in complex structural and infrastructure systems in which information evolves in time. Strategies for modeling and efficiently analyzing the eBN are described by way of several conceptual examples. The companion paper applies the eBN methodology to example structural and infrastructure systems

Open TURNS: An industrial software for uncertainty quantification in simulation

The needs to assess robust performances for complex systems and to answer tighter regulatory processes (security, safety, environmental control, and health impacts, etc.) have led to the emergence of a new industrial simulation challenge: to take uncertainties into account when dealing with complex numerical simulation frameworks. Therefore, a generic methodology has emerged from the joint effort of several industrial companies and academic institutions. EDF R&D, Airbus Group and Phimeca Engineering started a collaboration at the beginning of 2005, joined by IMACS in 2014, for the development of an Open Source software platform dedicated to uncertainty propagation by probabilistic methods, named OpenTURNS for Open source Treatment of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial challenges attached to uncertainties, which are transparency, genericity, modularity and multi-accessibility. This paper focuses on OpenTURNS and presents its main features: openTURNS is an open source software under the LGPL license, that presents itself as a C++ library and a Python TUI, and which works under Linux and Windows environment. All the methodological tools are described in the different sections of this paper: uncertainty quantification, uncertainty propagation, sensitivity analysis and metamodeling. A section also explains the generic wrappers way to link openTURNS to any external code. The paper illustrates as much as possible the methodological tools on an educational example that simulates the height of a river and compares it to the height of a dyke that protects industrial facilities. At last, it gives an overview of the main developments planned for the next few years

Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein–Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein–Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential