123,757 research outputs found
Rough convergence of sequences in a partial metric space
In this paper we have studied the notion of rough convergence of sequences in
a partial metric space. We have also investigated how far several relevant
results on boundedness, rough limit sets etc. which are valid in a metric space
are affected in a partial metric space.Comment: 12 page
Joint inversion scheme with an adaptive coupling strategy - applications on synthetic and real data sets
Joint inversion strategies for geophysical data have become increasingly popular since they allow to combine complementary information from different data sets in an efficient way. However, for joint inversion algorithms that use methods that are sensitive to different parameters it is important that they are not restricted to specific survey arrays and subsurface conditions. Hence, joint inversion schemes are needed that 1) adequately balance data from the different methods and 2) use links between the parameter models that are suited for a wide range of applications.
Here, we combine MT, seismic tomography and gravity data in a non-linear joint inversion that accounts for these critical issues. Data from the different methods are inverted separately and are joined through constrains accounting for parameter relationships. An advantage of performing the inversions separately (and not together in one matrix) is that no relative weighting between the data sets is required. To avoid that the convergence behavior of the inversions is profoundly disturbed by the coupling, the strengths of the associated constraints are re-adjusted at each iteration. As criteria to control the adaption of the coupling strengths we used a general version of the well-known discrepancy principle. Adaption of the coupling strengths makes the joint inversion scheme also applicable to subsurface conditions, for which the assumed relationships are only a rough first order approximation. So, the coupling between the different parameter models is automatically reduced if for some structures the true rock property behaviors differ significantly from the assumed relationships (e.g. the atypical density-velocity behavior of salt).
We have tested our scheme first on different synthetic 2-D models for which the assumed parameter relationships are everywhere valid. We observe that the adaption of the coupling strengths makes the convergence of the inversions very robust and that the final results are close to the true models. In a next step the scheme has been applied on models for which the assumed parameter relationships are invalid for some structures. For these structures deviations from the relationships are present in the final results; however, for the remaining structures the relative behaviors of the physical parameters are still approximately described by the assumed relationship. Finally, we applied our joint inversion scheme on seismic, MT and gravity data collected offshore the Faroe Islands, where basalt intrusions are present
Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise
Unique existence of solutions to porous media equations driven by continuous
linear multiplicative space-time rough signals is proven for initial data in
on bounded domains . The generation of a
continuous, order-preserving random dynamical system on and
the existence of a random attractor for stochastic porous media equations
perturbed by linear multiplicative noise in space and time is obtained. The
random attractor is shown to be compact and attracting in norm. Uniform bounds and uniform space-time continuity of
the solutions is shown. General noise including fractional Brownian motion for
all Hurst parameters is treated and a pathwise Wong-Zakai result for driving
noise given by a continuous semimartingale is obtained. For fast diffusion
equations driven by continuous linear multiplicative space-time rough signals,
existence of solutions is proven for initial data in .Comment: Published in at http://dx.doi.org/10.1214/13-AOP869 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The enhanced Sanov theorem and propagation of chaos
We establish a Sanov type large deviation principle for an ensemble of
interacting Brownian rough paths. As application a large deviations for the
(-layer, enhanced) empirical measure of weakly interacting diffusions is
obtained. This in turn implies a propagation of chaos result in rough path
spaces and allows for a robust subsequent analysis of the particle system and
its McKean-Vlasov type limit, as shown in two corollaries.Comment: 42 page
Autonomous clustering using rough set theory
This paper proposes a clustering technique that minimises the need for subjective
human intervention and is based on elements of rough set theory. The proposed algorithm is
unified in its approach to clustering and makes use of both local and global data properties to
obtain clustering solutions. It handles single-type and mixed attribute data sets with ease and
results from three data sets of single and mixed attribute types are used to illustrate the
technique and establish its efficiency
Deterministic homogenization for fast-slow systems with chaotic noise
Consider a fast-slow system of ordinary differential equations of the form
, , where it
is assumed that averages to zero under the fast flow generated by . We
give conditions under which solutions to the slow equations converge weakly
to an It\^o diffusion as . The drift and diffusion
coefficients of the limiting stochastic differential equation satisfied by
are given explicitly.
Our theory applies when the fast flow is Anosov or Axiom A, as well as to a
large class of nonuniformly hyperbolic fast flows (including the one defined by
the well-known Lorenz equations), and our main results do not require any
mixing assumptions on the fast flow.Comment: 31 page
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