Examinando por Autor "Collet, Pierre"

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    Ítem
    Asymptotics for the heat kernel in multicone domains
    (Academic Press Inc., 2016-02) Collet, Pierre; Duarte, Mauricio; Martínez, Servet; Prat-Waldron, Arturo; San Martín, Jaime
    A multicone domain Ω ⊆ Rn is an open, connected set that resembles a finite collection of cones far away from the origin. We study the rate of decay in time of the heat kernel p(t, x, y) of a Brownian motion killed upon exiting Ω, using both probabilistic and analytical techniques. We find that the decay is polynomial and we characterize limt→∞ t1+αp(t, x, y) in terms of the Martin boundary of Ω at infinity, where α > 0 depends on the geometry of Ω. We next derive an analogous result for tκ/2Px(T >t), with κ = 1 + α − n/2, where T is the exit time from Ω. Lastly, we deduce the renormalized Yaglom limit for the process conditioned on survival.
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    Harnessing evolutionary algorithms for enhanced characterization of ENSO events
    (Springer, 0025-01) Abdulkarimova, Ulviya; Abarca-del-Rio, Rodrigo; Collet, Pierre
    The El Niño-Southern Oscillation (ENSO) significantly influences the complexity and variability of the global climate system, driving its variability. ENSO events’ irregularity and unpredictability arise from intricate ocean–atmosphere interactions and nonlinear feedback mechanisms, complicating their prediction of timing, intensity, and geographic impacts. This study applies Genetic Programming and Genetic Algorithms within the EASEA (EAsy Specification of Evolutionary Algorithms) Evolutionary Algorithms (EA) framework to develop a repository of symbolic equations for El Niño and La Niña events, spanning their various intensities. By analyzing data from the Oceanic Niño Index, this approach yields equation-based characterizations of ENSO events. This methodology not only enhances ENSO characterization strategies but also contributes to expanding the use of EAs in climate event analysis. The resulting equations have the potential to offer insights beyond academia, benefiting education, climate policy, and environmental management. This highlights the importance of ongoing refinement, validation, and exploration in these fields through EAs. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.