We consider the symplectic Euler method for Hamiltonian systems with holonomic constraints and its generalizations to a class of overdetermined differential-algebraic equations (ODAEs) which are nonlinear in the algebraic variables. It is shown that a straightforward generalization of the symplectic Euler method is inconsistent. A different non-trivial generalization of the symplectic Euler met...

The Bootstrap resampling method may be efficiently used to estimate the generalization error of nonlinear regression models, as artificial neural networks and especially Least-square Support Vector Machines. Nevertheless, the use of the Bootstrap implies a high computational load. In this paper we present a simple procedure to obtain a fast approximation of this generalization error with a redu...

The bootstrap resampling method may be efficiently used to estimate the generalization error of nonlinear regression models, as artificial neural networks. Nevertheless, the use of the bootstrap implies a high computational load. In this paper we present a simple procedure to obtain a fast approximation of this generalization error with a reduced computation time. This proposal is based on empi...

Feature selection for classification working in high-dimensional feature spaces can improve generalization accuracy, reduce classifier complexity, and is also useful for identifying the important feature “markers”, e.g., biomarkers in a bioinformatics or biomedical context. For support vector machine (SVM) classification, a widely used feature selection technique is recursive feature eliminatio...

Low dimensional representations of images impose equivalence relations in the image space; the induced equivalence class of an image is named as its intrinsic generalization. The intrinsic generalization of a representation provides a novel way to measure its generalization and leads to more fundamental insights than the commonly used recognition performance, which is heavily influenced by the ...

Low dimensional representations of images impose equivalence relations in the image space; the induced equivalence class of an image is named as its intrinsic generalization. The intrinsic generalization of a representation provides a novel way to measure its generalization and leads to more fundamental insights than the commonly used recognition performance, which is heavily influenced by the ...

We present an isoperimetric inequality for a nonlinear generalization of the first twisted Dirichlet eigenvalue. Let λ(Ω) be the set functional defined by λ(Ω) = inf { ‖∇v‖Lp(Ω) ‖v‖Lq(Ω) , v ∈W }

A new system of coupled higher-order nonlinear Schrödinger equations is proposed which passes the Painlevé test for integrability well. A Lax pair and a multi-field generalization are obtained for the new system.

We obtain a new oscillation theorem for the nonlinear secondorder differential equation (a(t)x′(t))′ + p(t)f(t, x(t), x′(t)) + q(t)g(x(t)) = 0, t ∈ [0,∞), via the generalization of Leighton’s variational theorem.

Sufficient conditions are derived for the relative controllability of nonlinear neutral Volterra integrodifferential systems with distributed delays in the control variables. The results are a generalization of previous results and are obtained by using Schauder's fixed-point theorem.