We propose a principal curve tracing algorithm that uses the gradient and the Hessian of a given density estimate. Curve definition requires the local smoothness of data density and is based on the concept of subspace local maxima. Tracing of the curve is handled through the leading eigenvector where fixed-step updates are used. We also propose an image segmentation algorithm based on the origi...

The goal of this paper is to propose an improved competitive Hebbian learning for mode detection using a new activation function, to overcome its sensitivity to local irregularities in pattern distribution. This method is involved with an unsupervised clustering approach divided into four processing stages. It begins by the estimation of the probability density function, followed by a competiti...

This Letter presents a frequentist analysis of the hot and cold spots of the cosmic microwave background data collected by the Wilkinson Microwave Anisotropy Probe (WMAP). We compare the WMAP temperature statistics of extrema (number of extrema, mean excursion, variance, skewness and kurtosis of the excursion) to Monte Carlo simulations. We find that on average, the local maxima (high temperatu...

This paper presents a frequentist analysis of the hot and cold spots of the Cosmic Microwave Background (CMB) data collected by the Wilkinson Microwave Anisotropy Probe (WMAP). We compare the WMAP temperature statistics of extrema (number of extrema, mean excursion, variance, skewness and kurtosis of the excursion) to Monte-Carlo simulations. We find that, on average, the local maxima (high tem...

In this technical note, we describe and validate a topological false discovery rate (FDR) procedure for statistical parametric mapping. This procedure is designed to deal with signal that is continuous and has, in principle, unbounded spatial support. We therefore infer on topological features of the signal, such as the existence of local maxima or peaks above some threshold. Using results from...

BACKGROUND The geometry of the myocardium may influence changes in transmembrane potential (DeltaVm) during defibrillation. To test this hypothesis, specific nonlinear structures (bifurcations, expansions, and curved strands or "bends") were created in patterned cultures of neonatal rat myocytes. METHODS AND RESULTS Extracellular field stimuli (EFS; 7 to 11 V/cm field strength) were applied p...

We are developing a new problem-solving methodology based on a self-organization paradigm. To realize our future goal of self-organizing computational systems, we have to study computation based on local information and its emergent behavior, which are considered essential in self-organizing systems. This paper presents a stochastic (or nondeterministic) problem solving method using local opera...