In this paper, theoretical performance analysis of watermarking schemes based on correlation detection is undertaken, leading to a number of important observations on the watermarking system detection performance. Statistical properties of watermark sequences generated by piecewise-linear Markov maps are investigated. Correlation/spectral properties of such sequences are easily controllable, a ...

We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of “chaoticity”. The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorphisms, translations and skew translations. We then treat some discontinuous transformations such as the Baker map and the sawtooth-like maps. Our ap...

In this paper, statistical analysis of watermarking schemes based on correlation detection is presented. Statistical properties of watermark sequences generated by piecewise-linear Markov maps are exploited, resulting in superior watermark detection reliability. Correlation/spectral properties of such sequences are easily controllable, a fact that affects the watermarking system performance. A ...

Let A be an arbitrary symmetrizable Cartan matrix of rank r, and n = n+ be the standard maximal nilpotent subalgebra in the Kac-Moody algebra associated with A (thus, n is generated by E1, . . . , Er subject to the Serre relations). Let Ûq(n) be the completion (with respect to the natural grading) of the quantized enveloping algebra of n. For a sequence i = (i1, . . . , im) with 1 ≤ ik ≤ r, let...

In traditional over-the-counter (OTC) markets, investors trade bilaterally through intermediaries referred to as dealers. An important regulatory question is whether centralize OTC markets by shifting trades onto centralized platforms. We address this in the context of liquid Canadian government bond market. document that even market, dealers charge markups, and show there a price gap between l...

This is a survey of the results obtained by K. G lazek and his co-workers. We restrict our attention to the problems of axiomatizations of n-ary groups, classes of n-ary groups, properties of skew elements and homomorphisms induced by skew elements, constructions of covering groups, classifications and representations of n-ary groups. Some new results are added too.

In 1982/1983 A. Bichara and F. Mazzocca characterized the Grassmann space Gr(h,A) of index h of an affine space A of dimension at least 3 over a skew–field K by means of the intersection properties of the three disjoint families of maximal singular subspaces of Gr(h,A) and, till now, their result represents the only known characterization of Gr(h,A). If K is a commutative field and A has finite...

ly as 2-cochain: Fa = ρ ∗ ◦ 1 2 (θ − θ)∂i ∧ ∂k = ρ ◦ 1 2 (f )jlθ θ∂i ∧ ∂k (5.85) with θf = θf , or f ′ = 1 1 + fθ f, (5.86) 5.2. ORDINARY VERSUS NONCOMMUTATIVE GAUGE THEORY 99 which we recognize as the noncommutative field strength (with lower indices) for constant f , θ [128]. The general result for non-constant f , θ is thus simply obtained by the application of the covariantizing map ρ (afte...