Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well-known, ...

Most of a signal information is often carried by irregular structures and transient phenomena. The mathematical characterization of singularities with Lipschitz exponents is explained. Theorems are reviewed that estimate local Lipschitz exponents of functions from the evolution across scales of their wavelet transform. It is then proven that the local maxima of the wavelet transform modulus det...

Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavelet transform are explained. We then prove that the local maxima of a wavelet transform detect the ...

Stochastic local search is a successful technique in diverse areas of combinatorial optimisation and is predominantly applied to hard problems. When dealing with individual instances of hard problems, gathering information about specific properties of instances in a preprocessing phase is helpful for an appropriate parameter adjustment of local search-based procedures. In the present paper, we ...

We present a new method for automatic detection of peaks in noisy periodic and quasi-periodic signals. The new method, called automatic multiscale-based peak detection (AMPD), is based on the calculation and analysis of the local maxima scalogram, a matrix comprising the scale-dependent occurrences of local maxima. The usefulness of the proposed method is shown by applying the AMPD algorithm to...

Sorting problems have long been one of the foundations of theoretical computer science. Sorting problems attempt to learn properties of an unknown total order of a known set. We test the order by comparing pairs of elements, and through repeated tests deduce some order structure on the set. The set-maxima problem is: given a family S of subsets of a set X, produce the maximal element of each el...

This paper contain algorithm of a neocognitron neural network that has been trained to recognize segmentation of Image from color image. Corners and Edge contour extraction are segmentation by models of complex and end-stopped cells. Detection of corners and local edge maxima is performed by selection of local maxima in both edge and corner sub image. The advantage of the proposed model over ot...

Finding the Bayesian network that maximizes a score function is known as structure learning or structure discovery. Most approaches use local search in the space of acyclic digraphs, which is prone to local maxima. Exhaustive enumeration requires super-exponential time. In this paper we describe a “merely” exponential space/time algorithm for finding a Bayesian network that corresponds to a glo...

It is common knowledge that the EM algorithm can be trapped at local maxima and consequently fails to reach global maxima. We empirically investigate the severity of this problem in the context of hierarchical latent class (HLC) models. Our experiments were run on HLC models where dependency between neighboring variables is strong. (The reason for focusing on this class of models will be made c...