95 research outputs found
Three equivalent ordinal notation systems in cubical Agda
We present three ordinal notation systems representing ordinals below epsilon zero in type theory, using recent type-theoretical innovations such as mutual inductive-inductive definitions and higher inductive types. We show how ordinal arithmetic can be developed for these systems, and how they admit a transfinite induction principle. We prove that all three notation systems are equivalent, so that we can transport results between them using the univalence principle. All our constructions have been implemented in cubical Agda
Diffusion-induced vortex filament instability in 3-dimensional excitable media
We studied the stability of linear vortex filaments in 3-dimensional (3D)
excitable media, using both analytical and numerical methods. We found an
intrinsic 3D instability of vortex filaments that is diffusion-induced, and is
due to the slower diffusion of the inhibitor. This instability can result
either in a single helical filament or in chaotic scroll breakup, depending on
the specific kinetic model. When the 2-dimensional dynamics were in the chaotic
regime, filament instability occurred via on-off intermittency, a failure of
chaos synchronization in the third dimension.Comment: 5 pages, 5 figures, to appear in PRL (September, 1999
The Generic Model of Computation
Over the past two decades, Yuri Gurevich and his colleagues have formulated
axiomatic foundations for the notion of algorithm, be it classical,
interactive, or parallel, and formalized them in the new generic framework of
abstract state machines. This approach has recently been extended to suggest a
formalization of the notion of effective computation over arbitrary countable
domains. The central notions are summarized herein.Comment: In Proceedings DCM 2011, arXiv:1207.682
Konputazio-makinak eta adimena: '"Computing Machinery and Intelligence'". 1950. Mind 49 (236): 433-460.
Itzulpen hau A. M. Turingek, 1950ean, Mind aldizkarian '"Computing Machinery and Intelligence'" izenburupean argitaratutako bertsioarena da. Itzulpenaren lehenagoko bertsioa hemen argitaratu zen, 2003an: Gogoa III-2, 171-196 . [Bertsio berri hau Larraitz Zubeldiak eta Kepa Kortak orraztu dute]
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