The paper presents mathematical underpinnings of the locally linear embedding technique for data dimensionality reduction. It is shown that a cogent framework for describing the method is that of optimisation on a Grassmann manifold. The solution delivered by the algorithm is characterised as a constrained minimiser for a problem in which the cost function and all the constraints are defined on...

We examine various versions of Borel reducibility on equivalence relations on the Cantor space 2ω , using reductions given by Turing functionals on the inputs A ∈ 2ω . In some versions, we vary the number of jumps of A which the functional is allowed to use. In others, we do not require the reduction to succeed for all elements of the Cantor space at once, but only when applied to arbitrary fin...

Discovering and utilizing problem domain knowledge is a promising direction towards improving the efficiency of evolutionary algorithms (EAs) when solving optimization problems. We propose a knowledge-based variable reduction strategy (VRS) that can be integrated into EAs to solve unconstrained and first-order derivative optimization functions more efficiently. VRS originates from the knowledge...

In this paper, an intuitive analysis of a phase noise reduction technique is done, and then a modified structure is proposed to achieve higher phase noise reduction than the original one. This method reduces the impact of noise sources on the phase noise by decreasing closed-loop gain in zero-crossings points and moving this high closed-loop gain to the non-zero-crossings points. This reduction...