123,757 research outputs found

    Rough convergence of sequences in a partial metric space

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    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

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    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

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    Unique existence of solutions to porous media equations driven by continuous linear multiplicative space-time rough signals is proven for initial data in L1(O)L^1(\mathcal {O}) on bounded domains O\mathcal {O}. The generation of a continuous, order-preserving random dynamical system on L1(O)L^1(\mathcal {O}) 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 L∞(O)L^{\infty}(\mathcal {O}) norm. Uniform L∞L^{\infty} 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 Lm+1(O)L^{m+1}(\mathcal {O}).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

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    We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the (kk-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

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    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

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    Consider a fast-slow system of ordinary differential equations of the form x˙=a(x,y)+Δ−1b(x,y)\dot x=a(x,y)+\varepsilon^{-1}b(x,y), y˙=Δ−2g(y)\dot y=\varepsilon^{-2}g(y), where it is assumed that bb averages to zero under the fast flow generated by gg. We give conditions under which solutions xx to the slow equations converge weakly to an It\^o diffusion XX as Δ→0\varepsilon\to0. The drift and diffusion coefficients of the limiting stochastic differential equation satisfied by XX 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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