Browsing by Subject "Scientific discipline"

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    Diverse consequences of algorithmic probability
    (Springer, Berlin, Heidelberg, 2013) Özkural, Eray
    We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial intelligence, therefore establishing it as a rigorous scientific discipline. We also relate to our own work in incremental machine learning and philosophy of complexity. © 2013 Springer-Verlag Berlin Heidelberg.
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    Fast multipole methods in service of various scientific disciplines
    (IEEE, 2014) Gürel, Levent
    For more than two decades, several forms of fast multipole methods have been extremely successful in various scientific disciplines. Reduced complexity solutions are obtained for solving different forms of equations that are derived from Maxwell's equations, such as Helmholtz's equation for electrodynamics and Laplace's equation for electrostatics. Fast multipole solvers are developed for and applied to the integral equations derived from Helmholtz's and Laplace's equations. Fast multipole solvers are kernel-dependent techniques, i.e., they rely on certain analytical properties of the integral-equation kernels, such as diagonalizability. Electromagnetics is not the only discipline benefiting from the fast multipole methods; a plethora of computations in various disciplines, such as the solution of Schroedinger's equation in quantum mechanics and the calculation of gravitational force in astrophysics, to name a few, exploit the reduced-complexity nature of the fast multipole methods. Acoustics, molecular dynamics, structural mechanics, and fluid dynamics can be mentioned as other disciplines served by the fast multipole methods. © 2014 IEEE.