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...

Large-scale data mining and retrieval applications have increasingly turned to compact binary data representations as a way to achieve both fast queries and efficient data storage; many algorithms have been proposed for learning effective binary encodings. Most of these algorithms focus on learning a set of projection hyperplanes for the data and simply binarizing the result from each hyperplan...

Suppose that for a set H of n unknown hyperplanes in the Euclidean d-dimensional space, a line probe is available which reports the set of intersection points of a query line with the hyperplanes. Under this model, this paper investigates the complexity to nd a generic line for H and further to determine the hyperplanes in H. This problem arises in factoring the u-resultant to solve systems of ...

In this paper we present system Ltree for proposicional supervised learning. Ltree is able to define decision surfaces both orthogonal and oblique to the axes defined by the attributes of the input space. This is done combining a decision tree with a linear discriminant by means of constructive induction. At each decision node Ltree defines a new instance space by insertion of new attributes th...

We prove that, for each Banach space X which is isomorphic to its hyperplanes, the Lipschitz-free spaces over and sphere are isomorphic.

For the class of equalizers that employs a symbol-decision finite-memory structure with decision feedback, the optimal solution is known to be the Bayesian decision feedback equalizer (DFE). The complexity of the Bayesian DFE, however, increases exponentially with the length of the channel impulse response (CIR) and the size of the symbol constellation. Conventional Monte Carlo simulation for e...