170,492 research outputs found
Consistency properties of a simulation-based estimator for dynamic processes
This paper considers a simulation-based estimator for a general class of
Markovian processes and explores some strong consistency properties of the
estimator. The estimation problem is defined over a continuum of invariant
distributions indexed by a vector of parameters. A key step in the method of
proof is to show the uniform convergence (a.s.) of a family of sample
distributions over the domain of parameters. This uniform convergence holds
under mild continuity and monotonicity conditions on the dynamic process. The
estimator is applied to an asset pricing model with technology adoption. A
challenge for this model is to generate the observed high volatility of stock
markets along with the much lower volatility of other real economic aggregates.Comment: Published in at http://dx.doi.org/10.1214/09-AAP608 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
Accuracy of simulations for stochastic dynamic models
This paper provides a general framework for the simulation of stochastic dynamic models. Our analysis rests upon a continuity property of invariant distributions and a generalized law of large numbers. We then establish that the simulated moments from numerical approximations converge to their exact values as the approximation errors of the computed solutions converge to zero. These asymptotic results are of further interest in the comparative study of dynamic solutions, model estimation, and derivation of error bounds for the simulated moments
Analytical Determination of the Attack Transient in a Clarinet With Time-Varying Blowing Pressure
This article uses a basic model of a reed instrument , known as the lossless
Raman model, to determine analytically the envelope of the sound produced by
the clarinet when the mouth pressure is increased gradually to start a note
from silence. Using results from dynamic bifur-cation theory, a prediction of
the amplitude of the sound as a function of time is given based on a few
parameters quantifying the time evolution of mouth pressure. As in previous
uses of this model, the predictions are expected to be qualitatively consistent
with simulations using the Raman model, and observations of real instruments.
Model simulations for slowly variable parameters require very high precisions
of computation. Similarly, any real system, even if close to the model would be
affected by noise. In order to describe the influence of noise, a modified
model is developed that includes a stochastic variation of the parameters. Both
ideal and stochastic models are shown to attain a minimal amplitude at the
static oscillation threshold. Beyond this point, the amplitude of the
oscillations increases exponentially, although some time is required before the
oscillations can be observed at the '' dynamic oscillation threshold ''. The
effect of a sudden interruption of the growth of the mouth pressure is also
studied, showing that it usually triggers a faster growth of the oscillations
A graph-based aspect interference detection approach for UML-based aspect-oriented models
Aspect Oriented Modeling (AOM) techniques facilitate separate modeling of concerns and allow for a more flexible composition of these than traditional modeling technique. While this improves the understandability of each submodel, in order to reason about the behavior of the composed system and to detect conflicts among submodels, automated tool support is required. Current techniques for conflict detection among aspects generally have at least one of the following weaknesses. They require to manually model the abstract semantics for each system; or they derive the system semantics from code assuming one specific aspect-oriented language. Defining an extra semantics model for verification bears the risk of inconsistencies between the actual and the verified design; verifying only at implementation level hinders fixng errors in earlier phases. We propose a technique for fully automatic detection of conflicts between aspects at the model level; more specifically, our approach works on UML models with an extension for modeling pointcuts and advice. As back-end we use a graph-based model checker, for which we have defined an operational semantics of UML diagrams, pointcuts and advice. In order to simulate the system, we automatically derive a graph model from the diagrams. The result is another graph, which represents all possible program executions, and which can be verified against a declarative specification of invariants.\ud
To demonstrate our approach, we discuss a UML-based AOM model of the "Crisis Management System" and a possible design and evolution scenario. The complexity of the system makes con°icts among composed aspects hard to detect: already in the case of two simulated aspects, the state space contains 623 di®erent states and 9 different execution paths. Nevertheless, in case the right pruning methods are used, the state-space only grows linearly with the number of aspects; therefore, the automatic analysis scales
Gravitational waves from axisymmetrically oscillating neutron stars in general relativistic simulations
Gravitational waves from oscillating neutron stars in axial symmetry are
studied performing numerical simulations in full general relativity. Neutron
stars are modeled by a polytropic equation of state for simplicity. A
gauge-invariant wave extraction method as well as a quadrupole formula are
adopted for computation of gravitational waves. It is found that the
gauge-invariant variables systematically contain numerical errors generated
near the outer boundaries in the present axisymmetric computation. We clarify
their origin, and illustrate it possible to eliminate the dominant part of the
systematic errors. The best corrected waveforms for oscillating and rotating
stars currently contain errors of magnitude in the local wave
zone. Comparing the waveforms obtained by the gauge-invariant technique with
those by the quadrupole formula, it is shown that the quadrupole formula yields
approximate gravitational waveforms besides a systematic underestimation of the
amplitude of where and denote the mass and the radius of
neutron stars. However, the wave phase and modulation of the amplitude can be
computed accurately. This indicates that the quadrupole formula is a useful
tool for studying gravitational waves from rotating stellar core collapse to a
neutron star in fully general relativistic simulations. Properties of the
gravitational waveforms from the oscillating and rigidly rotating neutron stars
are also addressed paying attention to the oscillation associated with
fundamental modes
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