Results 1 to 10 of about 13,405 (148)

Algorithmic Probability-Guided Machine Learning on Non-Differentiable Spaces

Frontiers in Artificial Intelligence, 2021
We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this model-driven approach may require less training data and can potentially be more generalizable as
Santiago Hernández-Orozco, Santiago Hernández-Orozco, Hector Zenil, Hector Zenil, Hector Zenil, Hector Zenil, Jürgen Riedel, Jürgen Riedel, Adam Uccello, Narsis A. Kiani, Narsis A. Kiani, Jesper Tegnér   +11 more
doaj   +1 more source

Perturbative-Iterative Computation of Inertial Manifolds of Systems of Delay-Differential Equations with Small Delays

Algorithms, 2020
Delay-differential equations belong to the class of infinite-dimensional dynamical systems. However, it is often observed that the solutions are rapidly attracted to smooth manifolds embedded in the finite-dimensional state space, called inertial ...
Marc R. Roussel
doaj   +1 more source

Minimal Curvature Trajectories: Riemannian Geometry Concepts for Model Reduction in Chemical Kinetics [PDF]

, 2009
In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into ...
Lebiedz, Dirk, Reinhardt, Volkmar, Siehr, Jochen   +2 more
core   +2 more sources

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation [PDF]

, 2004
The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations.
Bluman G. W., Brazhnik P. K., Fokas A. S., M. LAKSHMANAN, M. SENTHILVELAN, Mathews P. M., Murphy G. M., Nucci M. C., P. S. BINDU, Qu C. Z., Qu C. Z., Scott A. C., Showalter K., Walgraef D., Whitham G. B.   +14 more
core   +3 more sources

The Cauchy atlas on the manifold of all complete ODE solutions

, 2003
In this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete solution of some differentiable first-order ordinary differential equation on the initial Cauchy condition are deduced. The result is obtained by studying the Cauchy atlas on a manifold of complete solutions.
Chladek, P., Klapka, L.
openaire   +2 more sources

Curvature flows for almost-hermitian Lie groups [PDF]

, 2014
We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad class of almost-hermitian ...
Lauret, Jorge
core   +3 more sources

Harmonic Forms and Spinors on the Taub-bolt Space [PDF]

, 2019
This paper studies the space of $L ^2 $ harmonic forms and $L ^2 $ harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a ...
Franchetti, Guido
core   +2 more sources

Elliptic CR-manifolds and shear invariant ODE with additional symmetries

, 2005
We classify the ODEs that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can be only 10 (for the quadric), 4 (for the listed examples) or less. This is in contrast
A. Chap, G. Schmalz, G. Schmalz, G. Schmalz, Gerd Schmalz, S. Lie, V.V. Ezhov, V.V. Ezhov, Vladimir Ezhov   +8 more
core   +2 more sources

Dynamical analysis and bifurcations in a fractional integrable equation

Alexandria Engineering Journal
This paper investigates the dynamics of the nonlinear (1+1)-dimensional integrable beta-fractional Akbota equation, a Heisenberg ferromagnet-type model essential for understanding curve analysis and surface geometry.
Hongwei Ma, Riaz Ur Rahman, Solomon Manukure   +2 more
doaj   +1 more source

M-theory and Seven-Dimensional Inhomogeneous Sasaki-Einstein Manifolds

, 2010
Seven-dimensional inhomogeneous Sasaki-Einstein manifolds $Y^{p,k}(KE_4)$ present a challenging example of AdS/CFT correspondence. At present, their field theory duals for $KE_4=\mathbb{CP}^2$ base are proposed only within a restricted range $3p/2\le k ...
A Butti, A Hanany, C Ahn, CN Pope, D Berenstein, D Fabbri, D Martelli, D Martelli, D Martelli, D Martelli, D Martelli, F Benini, H Kihara, Hyojoong Kim, J Bagger, J Kim, JH Lee, JP Gauntlett, JP Gauntlett, Jung Hun Lee, K Ueda, KA Intriligator, M Aganagic, M Bertolini, M Bertolini, M Cvetič, M Cvetič, MJ Duff, Nakwoo Kim, O Aharony, P Bozhilov, P Bozhilov, S Benvenuti, S Benvenuti, S Benvenuti, S Franco, S Franco, S Franco, SS Gubser, Sunchang Kim, T Oota, Y Imamura   +41 more
core   +1 more source