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...

The crystal of hydroxyapatite, Ca10 (PO4) 6 (OH) 2 has a characteristic that it varies easily depending on the acidic base environment around the enamel. The etymology of apatite is said to come from the Greek word meaning “to deceive” since it contains various elements in the Ca, PO4, and OH areas and changes appearance. In other words, the true character behind the demineralization and remine...

Automatic Dependent Surveillance-Broadcast (ADS-B) is an emerging software-defined radar technology that is supposed to replace current standards and is part of the Next Generation Transportation Systems (NextGen) in the US. In spite of its several benefits, this technology has been widely cited for being designed without security in mind, making it vulnerable to numerous attacks. Most approach...

A selection of aspects of the theory of bounded cohomology is presented. The emphasis is on questions motivating the use of that theory as well as on some concrete issues suggested by its study. Specific topics include rigidity, bounds on characteristic classes, quasification, orbit equivalence, amenability. Mathematics Subject Classification (2000). Primary 55N; Secondary 20F.