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...

Given a hyperplane arrangement A in a real vector space V , we introduce a real algebraic prevariety Z(A), and exhibit the complement ofA in the complexification of V as the total space of an affine bundle over Z(A) with fibers modeled on the dual vector space V . 1 Statement Let V be a real vector space of dimension d, and let f1, . . . , fn be a collection of nonconstant affine linear functio...

Maximal margin classifiers are a core technology in modern machine learning. They have strong theoretical justifications and have shown empirical successes. We provide an alternative justification for maximal margin hyperplane classifiers by relating them to Bayes optimal classifiers that use Parzen windows estimations with Gaussian kernels. For any value of the smoothing parameter (the width o...

Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of nondegenerate hyperplane codes, in terms of the polar complex of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a non-degenerate hyperplane code is shellable and show that all cu...

Given a set S of n ≥ d points in general position in Rd, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree is a binary space partition tree obtained by recursive application of random hyperplane splits. We investigate the structural distributions of such random trees...

The Tutte polynomial is a fundamental invariant associated to a graph, matroid, vector arrangement, or hyperplane arrangement, which answers a wide variety of questions about its underlying object. This short survey focuses on some of the most important results on Tutte polynomials of hyperplane arrangements. We show that many enumerative, algebraic, geometric, and topological invariants of a h...

The requirement of transformation invariance of a probability distribution is employed to derive prior probabilities for the coefficients of the equation describing a hyperplane. In two dimensions, this is a straight line, in three dimensions an ordinary plane etc. We treat the general case of n dimensions and propose a procedure to normalize the resulting distributions in order to make them pr...