In this paper, we derive some of the stochastic properties of a universal linear predictor, through analyses similar to those generally made in the adaptive signal processing literature. In [l], a predictor was introduced whose sequentially accumulated mean squared error for any bounded individual sequence was shown to be as small as that for any linear predictor of order less than some maximum...

Principal curves are parameterized curves passing “through the middle” of a data cloud. These objects constitute a way of generalization of the notion of first principal component in Principal Component Analysis. Several definitions of principal curve have been proposed, one of which can be expressed as a least-square minimization problem. In the present paper, adopting this definition, we stud...

In the paper an upper bound is established for certain exponential sums, analogous to Gaussian sums, defined on the points of an elliptic curve over a prime finite field. The bound is applied to prove the existence of group generators for the set of points on an elliptic curve over Fq among certain sets of bounded size. We apply this estimate to obtain a deterministic O(q) algorithm for finding...

Longslit spectroscopy is entering an era of increased spatial and spectral resolution and increased sample size. Improved instruments reveal complex velocity structure that cannot be described with a one-dimensional rotation curve, yet samples are too numerous to examine each galaxy in detail. Therefore, one goal of rotation curve measurement techniques is to flag cases in which the kinematic s...

The Otsu s method has been proven as an efficient method in image segmentation for bi-level thresholding. However, this method is computationally intensive when extended to multi-level thresholding. In this paper, we present a hybrid optimization scheme for multiple thresholding by the criteria of (1) Otsu s minimum within-group variance and (2) Gaussian function fitting. Four example images ar...

Longslit spectroscopy is entering an era of increased spatial and spectral resolution and increased sample size. Improved instruments reveal complex velocity structure that cannot be described with a one-dimensional rotation curve, yet samples are too numerous to examine each galaxy in detail. Therefore, one goal of rotation curve measurement techniques is to ag cases in which the kinematic str...

Differences in reaction time (RT) variability have been documented between children with and without Attention Deficit Hyperactivity Disorder (ADHD). Most previous research has utilized estimates of normal distributions to examine variability. Using a nontraditional approach, the present study evaluated RT distributions on the Conners' Continuous Performance Test in children and adolescents fro...

The development of risk management methodologies for non-gaussian markets relies often on the assumption that the underlying market factors have a gaussian distribution. While advances have been made in the modeling of more general marginal distributions of the risk factors, the modeling of non-gaussian dependence structures is much less advanced. For commodities markets that often exhibit sudd...

This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best-fit copula. Thereafter, simulation of copulas and bivariat...

Let X(0) be an unknown M by N matrix. In matrix recovery, one takes n < MN linear measurements y(1),…,y(n) of X(0), where y(i) = Tr(A(T)iX(0)) and each A(i) is an M by N matrix. A popular approach for matrix recovery is nuclear norm minimization (NNM): solving the convex optimization problem min ||X||*subject to y(i) =Tr(A(T)(i)X) for all 1 ≤ i ≤ n, where || · ||* denotes the nuclear norm, name...