13,896 research outputs found
Tropical Geometry and the Motivic Nearby Fiber
We construct motivic invariants of a subvariety of an algebraic torus from
its tropicalization and initial degenerations. More specifically, we introduce
an invariant of a compactification of such a variety called the "tropical
motivic nearby fiber." This invariant specializes in the schon case to the
Hodge-Deligne polynomial of the limit mixed Hodge structure of a corresponding
degeneration. We give purely combinatorial expressions for this Hodge-Deligne
polynomial in the cases of schon hypersurfaces and smooth tropical varieties.
We also deduce a formula for the Euler characteristic of a general fiber of the
degeneration.Comment: 27 pages. Compositio Mathematica, to appea
Permporometry: the determination of the size distribution of active pores in UF membranes
Permporometry is a method by which the characteristics of the interconnecting 'active' pores of an ultrafiltration membrane can be measured. It is these active' pores that are responsible for the actual membrane performence. Application of permporometry on different membrane types, including ceramic as well as polymeric membranes, shows that the method can provide objective information on the `active¿ pore size present
Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution
In this paper we perform an analytical and numerical study of Extreme Value
distributions in discrete dynamical systems. In this setting, recent works have
shown how to get a statistics of extremes in agreement with the classical
Extreme Value Theory. We pursue these investigations by giving analytical
expressions of Extreme Value distribution parameters for maps that have an
absolutely continuous invariant measure. We compare these analytical results
with numerical experiments in which we study the convergence to limiting
distributions using the so called block-maxima approach, pointing out in which
cases we obtain robust estimation of parameters. In regular maps for which
mixing properties do not hold, we show that the fitting procedure to the
classical Extreme Value Distribution fails, as expected. However, we obtain an
empirical distribution that can be explained starting from a different
observable function for which Nicolis et al. [2006] have found analytical
results.Comment: 34 pages, 7 figures; Journal of Statistical Physics 201
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