A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding the hypothesis error from the sum automatically. Following this direction, we ...

We present a novel online learning paradigm for nonlinear function estimation based on iterative orthogonal projections in an L space reflecting the stochastic property of input signals. An online algorithm is built upon the fact that any finite dimensional subspace has a reproducing kernel, which is given in terms of the Gram matrix of its basis. The basis used in the present study involves mu...

We hypothesize that life began not with the first self-reproducing molecule or metabolic network, but as a prebiotic ecology of co-evolving populations of macromolecular aggregates (composomes). Each composome species had a particular molecular composition resulting from molecular complementarity among environmentally available prebiotic compounds. Natural selection acted on composomal species ...

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear c...

The purpose of this paper is to reveal the deep and rich structure of the set of Parseval frame wavelets. Two main directions are pursued. First, we study the reproducing properties of the translates of a Parseval frame wavelet within the closed linear span that the translates generate. In particular, we show that the translates need not have good reproducing properties, even though the transla...

A reproducing kernel Hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. In this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. The analytical solution is represented in the form of series in the reproducing kernel space. Some numerical ...

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It’s well-known that reproducing kernel (R.K) is a useful kernel function ...

and Applied Analysis 3 2. Several Reproducing Kernel Spaces In this section, several reproducing kernels needed are constructed in order to solve 1.1 and 1.2 using RKHSmethod. Before the construction, we utilize the reproducing kernel concept. Throughout this paper C is the set of complex numbers, L2 a, b {u | ∫b a u2 x dx < ∞}, l2 {A | ∑∞i 1 Ai 2 < ∞}, and the superscript n in u n t denotes th...

In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Ca...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...