| We propose a novel criterion of deciding time delays for reconstructing attractors from a single variable time series. Our criterion considers higher order correlation functions, and nds the convergence values of the extrema. In order to see how our method works well, we analyze two numerical examples by observing the shapes of reconstructed attractors and calculating phase space continuities...

We present a new unified proof for the convergence of both the Jacobi and the Gauss–Seidel methods for solving systems of linear equations under the criterion of either (a) strict diagonal dominance of the matrix, or (b) diagonal dominance and irreducibility of the matrix. These results are well known. The proof for criterion (a) makes use of Geršgorin’s theorem, while the proof for criterion (...

We investigate under what conditions a neuron can learn by experimentally supported rules for spike timing dependent plasticity (STDP) to predict the arrival times of strong “teacher inputs” to the same neuron. It turns out that in contrast to the famous Perceptron Convergence Theorem, which predicts convergence of the perceptron learning rule for a strongly simplified neuron model whenever a s...

Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (MSE) criterion, which is an ideal optimality criterion under Gaussian noises....

We introduce and develop a pathwise description of the dissipation of general convex entropies for continuous time Markov processes, based on simple backward martingales and convergence theorems with respect to the tail sigma field. The entropy is in this setting the expected value of a backward submartingale. In the case of (non necessarily reversible) Markov diffusion processes, we use Girsan...

Sparse system identification has received a great deal of attention due to its broad applicability. The proportionate normalized least mean square (PNLMS) algorithm, as a popular tool, achieves excellent performance for sparse system identification. In previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the mean square error (MSE) crit...

We are concerned with eigenvalue problems for definite and indefinite symmetric matrix pencils. First, Rayleigh-Ritz methods are formulated and, using Krylov subspaces, a convergence analysis is presented for definite pencils. Second, generalized symmetric Lanczos algorithms are introduced as a special Rayleigh-Ritz method. In particular, an a posteriori convergence criterion is demonstrated by...

Generally, the blind separation algorithms based on the subspace approach are very slow. In addition, they need a considerable computation e ort and time due to the estimation and the minimization of huge matrices. Previously, we proposed an adaptive subspace criterion to solve the blind separation problem [1]. The criterion has been minimized adaptively using a conjugate gradient algorithm [2]...

The authors argue that commonly used ranking and rating methods of value surveys may have low validity in cross-cultural value comparisons because participants' reports about values can be affected by factors such as cultural differences in the meaning of particular value terms as well as the possibility that some value judgments are based on social comparison or deprivation rather than on any ...

Conventional training of a hidden Markov model (HMM) is performed by an expectation-maximization algorithm using a maximum likelihood (ML) criterion. Recently it was reported that, using an incremental variant of maximum a posteriori estimation, substantial speed improvements could be obtained. The approach requires a prior distribution when the training starts, although it is diicult to nd an ...