356 research outputs found
Anomalous jumping in a double-well potential
Noise induced jumping between meta-stable states in a potential depends on
the structure of the noise. For an -stable noise, jumping triggered by
single extreme events contributes to the transition probability. This is also
called Levy flights and might be of importance in triggering sudden changes in
geophysical flow and perhaps even climatic changes. The steady state statistics
is also influenced by the noise structure leading to a non-Gibbs distribution
for an -stable noise.Comment: 11 pages, 7 figure
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
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
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
Correlation regimes in fluctuations of fatigue crack growth
This paper investigates correlation properties of fluctuations in fatigue
crack growth of polycrystalline materials, such as ductile alloys, that are
commonly encountered in structures and machinery components of complex
electromechanical systems. The model of crack damage measure indicates that the
fluctuations of fatigue crack growth are characterized by strong correlation
patterns within short time scales and are uncorrelated for larger time scales.
The two correlation regimes suggest that the 7075-T6 aluminum alloy, analyzed
in this paper, is characterized by a micro-structure which is responsible for
an intermittent correlated dynamics of fatigue crack growth within a certain
scale. The constitutive equations of the damage measure are built upon the
physics of fracture mechanics and are substantiated by Karhunen-Lo\`{e}ve
decomposition of fatigue test data. Statistical orthogonality of the estimated
damage measure and the resulting estimation error is demonstrated in a Hilbert
space setting.Comment: 30 pages, 8 figures, to appear in Physica
Responses of Leaky Integrate-and-Fire Neurons to a Plurality of Stimuli in Their Receptive Fields
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
Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond
We present a simple construction method for Feller processes and a framework
for the generation of sample paths of Feller processes. The construction is
based on state space dependent mixing of L\'evy processes.
Brownian Motion is one of the most frequently used continuous time Markov
processes in applications. In recent years also L\'evy processes, of which
Brownian Motion is a special case, have become increasingly popular.
L\'evy processes are spatially homogeneous, but empirical data often suggest
the use of spatially inhomogeneous processes. Thus it seems necessary to go to
the next level of generalization: Feller processes. These include L\'evy
processes and in particular Brownian motion as special cases but allow spatial
inhomogeneities.
Many properties of Feller processes are known, but proving the very existence
is, in general, very technical. Moreover, an applicable framework for the
generation of sample paths of a Feller process was missing. We explain, with
practitioners in mind, how to overcome both of these obstacles. In particular
our simulation technique allows to apply Monte Carlo methods to Feller
processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the
generation of sample paths of Feller processe
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