Classic complexity theory indicates that a large number of natural combinatorial problems are inherently hard to solve algorithmically (in technical terms, they are NP-hard and, thus, it is not expected that they admit a polynomial time algorithm). The parameterization idea tries to cope with this rather discouraging fact by asking whether it is possible to to design algorithms where the non-po...

We describe quantum tomography as an inverse statistical problem. We show results of consistency in different norms, for Pattern Function Projection Estimators as well as for Sieve Maximum Likelihood Estimators for the density matrix of the quantum state and its Wigner function. The density matrix and the Wigner function are two different ways of representing quantum state. Results are derived ...

This report is Chapter 1 in the author’s book Qualitative Computing: A computational journey into non linearity published by World Scientific, Singapore (2011). It presents an historical survey of the evolution of mathematical computation since Sumer four millennia ago. It shows how the laws of logic have evolved in the mind of mathematicians. This evolution has been driven by three major ideas...

Semigroups with an additional unary operation called a (right) closure are investigated. These “closure semigroups” may be viewed as (not necessarily regular) generalisations of inverse semigroups, and several powerful structural aspects of inverse semigroup theory are shown to extend naturally to some important classes of closure semigroups. These include representations as partial transformat...