Kant's Transcendental Distinction

KANTS: Artifical Ant System for Classification

This paper investigates a new model that takes advantage of the cooperative self-organization of Ant Algorithms to evolve a naturally inspired pattern recognition (and also clustering) method. The approach considers each data item as an ant that changes the environment as it moves through it. The algorithm is successfully applied to well-known classification problems and yields better results t...

Transcendental Elitism

KANTS – A Stigmergic Algorithm for Data Clustering and Swarm Art

KANTS is a swarm intelligence algorithm [1], proposed in [10, 2] for data clustering and classification. The term KANTS derives from Kohonen Ants, since the algorithm was partially inspired by Kohonen’s Self-Organizing Maps [9]. The method was also based on Chialvo and Millonas’ Ant System [6] and its working mechanisms are very similar to that model. However, differences in the local rules and...

On Transcendental Numbers

Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them. New inequalities for transcendental numbers are stated in Section 2 and proved in Section 4. Also, in relationship with these topics, we study the exponential function axioms related to the Yang-Baxter equation.

Algebraic and Transcendental Numbers

To begin with, recall that a complex number α is said to be a root of a polynomial P (X) if P (α) = 0. A complex number α is said to be algebraic if there is a nonzero polynomial P (X), with integer coefficients, of which α is a root. The set of algebraic numbers is denoted by Q̄. A complex number α which is not algebraic is said to be transcendental. The following numbers are obviously algebrai...