vii List of Figures xiii

We consider autoreducibility of complete sets for the two common types of probabilistic polynomial-time reductions: RP reductions containing one-sided errors on positive input instances only, and BPP reductions containing two-sided errors. Specifically, we focus on the probabilistic counterparts of the deterministic many-one and truthtable autoreductions. We prove that non-trivial complete sets...

Based on the empirical or theoretical qualitative information about the relationship between response variable and covariates, we propose a new approach to model polynomial regression using a shape restricted regression after estimating the direction by sufficient dimension reduction. The purpose of this paper is to illustrate that in the absence of prior information other than the shape constr...

We reconsider the Nagelian theory of reduction and argue that, contrary to a widely held view, it is the right analysis of intertheoretic reduction. The alleged difficulties of the theory either vanish upon closer inspection or turn out to be substantive philosophical questions rather than knock-down arguments.

Invited for this month's cover picture is the group of Professor Toribio F. Otero at the Centre for Electrochemistry, Intelligent Materials and Devices at the Polytechnic University of Cartagena (Spain). The cover picture shows an electrochemical cell as well as three representative cyclic voltammetric responses, displaying the electrolyte potential window, the monomer oxidation-polymerization ...

The ever-growing amount of data stored in digital databases raises the question of how to organize and extract useful knowledge. This paper outlines some current developments in the domains of dimensionality reduction, manifold learning, and topological learning. Several aspects are dealt with, ranging from novel algorithmic approaches to their realworld applications. The issue of quality asses...

LLE(Local linear embedding) is a widely used approach for dimension reduction. The neighborhood selection is an important issue for LLE. In this paper, the ε-distance approach and a slightly modified version of k-nn method are introduced. For different types of datasets, different approaches are needed in order to enjoy higher chance to obtain better representation. For some datasets with compl...