The dynamical and stationary properties of on-line learning from finite training sets are analyzed by using the cavity method. For large input dimensions, we derive equations for the macroscopic parameters, namely, the student-teacher correlation, the student-student autocorrelation and the learning force fluctuation. This enables us to provide analytical solutions to Adaline learning as a benc...

A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent...

We design adaptive high-order Galerkin methods for the solution of linear elliptic problems and study their performance. We start by considering adaptive Fourier-Galerkin methods and Legendre spectralelement methods, which offer unlimited approximation power only restricted by solution and data regularity. We next turn our attention to the $hp$-version of the finite element method, for which we...

In the simulation of the NC-shape grinding process, a finite element model of the grinding machine is included. To enhance the accuracy and efficiency of the finite element computation, a posteriori error estimation and resulting adaptive mesh refinement techniques are used. In this note, a dual weighted a posteriori error estimate for a linear second order hyperbolic model problem is derived. ...

order accurate discontinuous discontinuous nite element solution of the 2D Euler equations, A massively parallel adaptive nite element method with dynamic load balancing, SAND 93-0936C (1993). 21. K. Eriksson and C. Johnson, Adaptive nite element methods for parabolic problems I: A linear model problem, SIAM J. Adaptive nite element methods for parabolic problems IV: A nonlinear model problem, ...

Proofs of convergence of adaptive finite element methods for approximating eigenvalues and eigenfunctions of linear elliptic problems have been given in a several recent papers. A key step in establishing such results for multiple and clustered eigenvalues was provided by Dai et. al. in [8], who proved convergence and optimality of AFEM for eigenvalues of multiplicity greater than one. There it...

ADALINE model to predict floor pressures in a subsonic cavity flow Mehmet Önder Efe, Marco Debiasi, Peng Yan, Hitay Özbay and Mohammad Samimy Department of Electrical and Electronics Engineering, TOBB Economics and Technology University, Sögütözü Ankara, Turkey National University of Singapore, Temasek Laboratories, Singapore Enterprise Servo Engineering, Seagate Technology, Shakopee, MN 55379,...

concrete bridge deck damage detection by measurement and monitoring variables related to vibration signatures is one of the main tasks of any bridge health monitoring system (bhms). generally damage puts some detectable/discoverable signs in the parameters of bridge vibration behavior. however, differences between frequency and mode shape before and after damage are not remarkable as vibration ...