The processing performed by a feed-forward neural network is oft en int erpreted through use of decision hyperplanes at each layer. T he adaptation process, however, is normally explained using the picture of gradient descent of an error land scape. In thi s paper t he dynamics of t he decision hyperplanes is used as t he model of the adaptat ion process. An electro-mechanical analogy is drawn ...

In this paper we investigate the combinatorial complexity of an algorithm to determine the geometry and the topology related to an arrangement of hyperplanes in multi-dimensional Euclidean space from the “probing” on the arrangement. The “probing” by a flat means the operation from which we can obtain the intersection of the flat and the arrangement. For a finite set H of hyperplanes in Ed, we ...

A signal space partitioning technique is presented for detecting symbols transmitted through intersymbol interference channels. The decision boundary is piecewise linear and is made up of several hyperplanes. The goal here is to minimize the number of hyperplanes for a given performance measure, namely, the minimum distance between any signal and the decision boundary. Unlike in Voronoi partiti...

In the paper [8], we introduced the notions of pseudo-hyperplane and pseudoembedding of a point-line geometry and proved that every generalized quadrangle of order (s, t), 2 ≤ s <∞, has faithful pseudo-embeddings. The present paper focuses on generalized quadrangles of order (3, t). Using the computer algebra system GAP [12] and invoking some theoretical relationships between pseudo-hyperplanes...

|A signal-space detector estimates the channel input symbol based on the location of the nite-length observation signal in a multi-dimensional signal-space. The decision boundary is formed by a set of hyperplanes. The resulting detector structure consists of linear discriminant functions, threshold detectors, and a Boolean logic function. Our goal is to minimize the number of linear discriminan...

After a review on asymptotic flatness, a general discussion of asymptotic weak and strong Poincaré charges in metric gravity is given with special emphasis on the boundary conditions needed to define the proper Hamiltonian gauge transformations and to get a differentiable Dirac Hamiltonian. Lapse and shift functions are parametrized in a way which allows to identify their asymptotic parts with ...

For analysing k-variate data sets, Randles (1989) considered hyperplanes going through k− 1 data points and the origin. He then introduced an empirical angular distance between two k-variate data vectors based on the number of hyperplanes (the so-called interdirections) that separate these two points, and proposed a multivariate sign test based on those interdirections. In this paper, we presen...

Let ∆ be a symplectic dual polar space DW (2n−1, K) or a Hermitian dual polar space DH(2n − 1, K, θ), n ≥ 2. We define a class of hyperplanes of ∆ arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space DH(2n−1, K, θ) arising from its Grassmann-...

In this paper we present some theoretical results on two forms of multi-point crossover: n-point crossover and uniform crossover. This analysis extends the work from De Jong’s thesis, which dealt with disruption of n-point crossover on 2nd order hyperplanes. We present various extensions to this theory, including 1) an analysis of the disruption of n-point crossover on kth order hyperplanes; 2)...

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperp...