Consider the problem of estimating the centers µ = (µ 1 ,. .. , µ k) of a uniform mixture of unit-variance spherical Gaussians in R d , k i=1 1 k 1 (2π) d/2 e |x−µi| 2 /2 , x m drawn from this distribution. This can be done by maximizing the (average log) likelihood L (x1,...,xm) (µ) = 1 m i log f µ (x i). Maximizing the likelihood is guaranteed to recover the correct centers, in the large-samp...

We give an upper bound in O(d) for the number of critical points of a normal random polynomial. The number of minima (resp. maxima) is in O(d)Pn, where Pn is the (unknown) measure of the set of symmetric positive matrices in the Gaussian Orthogonal Ensemble GOE(n). Finally, we give a closed form expression for the number of maxima (resp. minima) of a random univariate polynomial, in terms of hy...

This paper deals with power-quality (PQ) event detection, classification and characterization using higher-order sliding cumulants to examine the signals. Their maxima and minima are the main features, and the classification strategy is based in competitive layers. Concretely, we concentrate on the task of differentiating two types of transients (short duration and long duration). By measuring ...

We give an upper bound in O(d) for the number of critical points of a normal random polynomial. The number of minima (resp. maxima) is in O(d)Pn, where Pn is the (unknown) measure of the set of symmetric positive matrices in the Gaussian Orthogonal Ensemble GOE(n). Finally, we give a closed form expression for the number of maxima (resp. minima) of a random univariate polynomial, in terms of hy...

We propose a set of techniques for extracting a new standard benchmark database for Arabic handwritten scripts. Thresholding, filtering, and skew detection/correction techniques are developed as a pre-processing step of the database. Local minima and maxima using horizontal and vertical histogram are implemented for extracting the script elements of the database. Elements of the database contai...

Multiple Fault Diagnosis (MFD) is the process of determining the correct fault or faults that are responsible for a given set of symptoms. MFD problems are generally characterized by problem-spaces containing many local minima and maxima. We show that when using Genetic Algorithms to solve these kinds of problems, best results can be achieved with higher than \normal" mutation rates. Schemata t...

We give a detailed derivation of a generalization of the second derivative test of single-variable calculus which can classify critical points as local minima or local maxima (or neither), whenever the traditional second derivative test fails, by considering the values of higher-order derivatives evaluated at the critical points. The enhanced test is local, in the sense that it is only necessar...