The traditional crossover operator used in genetic search exhibits a position-dependent bias called the dcfining-length bias. We show how this bias results in hidden biases that are difficult to anticipate and compensate for. We introduce a new crossover operator, shuffle crossover, that eliminates the position dependent bias of the traditional crossover operator by shuffling the representation...

For diagonal cubic surfaces, we give an upper bound for E. Peyre’s Tamagawa type number in terms of the coefficients of the defining equation.

This article critically analyses the Longman Defining Vocabulary (LDV) in relation to its size, range and frequency, senses, parts of speech, affixes, and multiword expressions. The recent versions of the LDV contain a relatively fixed number of items. Over 85% of those items were found to be highly frequent, and for the defining purpose, genus terms, grammatical terms, etc. have also been incl...

This paper provides insights into the role of symmetry in studying polynomial functions vanishing to high order on an algebraic variety. The varieties we study are singular loci hyperplane arrangements projective space, with emphasis arising from complex reflection groups. We provide minimal sets equations for radical ideals defining these and containments between ordinary symbolic powers ideal...

Hyperplane arrangements are very interesting combinatorial objects and many results can be found in the literature. For instance, several papers [1, 2, 6, 7] are concerned with the characteristic polynomials and the number of regions of a hyperplane arrangement. In his paper [9], Stanley reviewed various hyperplane arrangements raising interesting questions, one of which is related to the follo...

in seismic exploration studies different types of techniques are used to recognize seismic features in terms of their temporal and spatial spectra. variations in frequency content are sensitive to subtle changes in reflection information (castro de matos et al., 2003). in this study the joint time-frequency analysis is used for seismic texture recognition. discrete wavelet transform (dwt) witho...

We study (i-)locally singular hyperplanes in a thick dual polar space of rank n. If is not of type DQ(2n,K), then we will show that every locally singular hyperplane of is singular. We will describe a new type of hyperplane in DQ(8,K) and show that every locally singular hyperplane of DQ(8,K) is either singular, the extension of a hexagonal hyperplane in a hex or of the new type. © 2005 Elsevie...

This lecture is about a special type of optimization problems, namely linear programs. We start with a geometric problem that can directly be formulated as a linear program. Let P ⊆ R d and Q ⊆ R d be two finite point sets in d-dimensional space. We want to know whether there exists a hyperplane that separates P from Q (we allow non-strict separation, i.e. some points are allowed to be on the h...