Methods Explained

Sums of Squares Methods Explained: Part I

Let p(~x) ∈ R[~x] be SOS in t real polynomial squares. Then, p(~x) must have even degree. Let deg(p(~x)) = 2k. Then, ∃q1, . . . , qt ∈ R[~x] s.t. deg(qi(~x)) ≤ k and p(~x) = ∑t i=1 q 2 i (~x). A key observation is that we can now exactly characterise the finitely many possible power-products that could occur in each qi(~x). Definition 1.1. Let Λn(d) = {α = 〈α1, . . . , αn〉 ∈ Nn | α1 + . . .+ αn...

2FA ONE: Security Model and Authentication Methods Explained

Nonuniversality explained

The Nonuniversality in Computation Theorem (NCT) states that no computer capable of a finite and fixed number of basic operations per time unit can be universal. This result, obtained in 2005, disproves major prevailing dogmas in computer science, on the strength of several counterexamples that differ significantly from one another. Thus, the NCT shows that the Church-Turing Thesis (CTT) is fal...

Genius explained

The physician's art is the catalogue of an exhibition of over 100 images and other objects from the collections of four North Carolina medical schools. In a finely-judged Preface, structured around specific examples shown, Martin Kemp points out some of the historical issues involved in the study of medical imagery and artifacts, beginning with the problem of what "realism" means in the context...

Strategies Explained

the 5th Game Programming Workshop in Japan, 1999 TR-99-32 Re eived 07 O t 99 Strategies Explained Ian Frank Ele trote hni al Laboratory Ma hine Inferen e Group Umezono 1-1-4, Tsukuba Ibaraki, JAPAN 305 David Basin Institut f ur Informatik Universitat Freiburg Am Flughafen 17 Freiburg, Germany Abstra t For many problem-solving tasks, it is important not only to produ e solutions, but also to j...