In this paper we embed m-dimensional Euclidean space in the geometric algebra Clm to extend the operators of incidence in R to operators of incidence in the geometric algebra to generalize the notion of separator to a decision boundary hyperconic in the Clifford algebra of hyperconic sections denoted as Cl(V2). This allows us to extend the concept of a linear perceptron or the spherical percept...

A theoretical testing method for fully characterising the Mooney-Rivlin three-parameter hyper-elastic material model is proposed by capturing full-field digital image correlation (DIC) data, namely displacement field and indentation force data. finite element with known parameters will act as experimental against which all data be referenced (a preliminary test case). Going forward this stand-i...

The trace properties of the sample paths of suuciently regular generalized random elds are studied. In particular, nice localisation properties are shown in the case of hyperplanes. Using techniques of Euclidean quantum eld theory a constructive description of the conditional expectation values with respect to some Gibbs measures describing Euclidean quantum eld theory models and the-algebras l...

Given a set of n hyperplanes h1, . . . , hn ∈ R d the hyperplane depth of a point P ∈ R is the minimum number of hyperplanes that a ray from P can meet. The hyperplane depth of the arrangement is the maximal depth of points P not in any hi. We give an optimal O(n logn) deterministic algorithm to compute the hyperplane depth of an arrangement in dimension d = 2.

The trace properties of the sample paths of su ciently regular generalized random elds are studied. In particular, nice localisation properties are shown in the case of hyperplanes. Using techniques of Euclidean quantum eld theory a constructive description of the conditional expectation values with respect to some Gibbs measures describing Euclidean quantum eld theory models and the -algebras ...

In this paper, we formulate and investigate the following problem: given integers d, k and r where k > r ≥ 1, d ≥ 2, and a prime power q, arrange d hyperplanes on Fq to maximize the number of r-dimensional subspaces of Fq each of which belongs to at least one of the hyperplanes. The problem is motivated by the need to give tighter bounds for an error-tolerant pooling design based on finite vect...