Blind spread-spectrum watermarking schemes with correlation based detection algorithms suffer significantly from host signal interference. Improvements are possible when considering the host signal as side-information to the watermark encoder. Costa showed that, in a specific case, host signal interference can be avoided completely. The scalar Costa scheme, which operates on structured codebook...

The fundamental group is an invariant of topological spaces that measures the contractibility of loops. This project studies the fundamental group, its basic properties, some elementary computations, and a resulting theorem: the Fixed Point Theorem of Brouwer, which states that every continuous function mapping the disk to itself has a fixed point.

A BSS machine is δ-uniform if it does not use exact tests; such machines are equivalent (modulo parameters) to Type 2 Turing machines. We define a notion of closure related to Turing machines for archimedean fields, and show that such fields admit nontrivial δ-uniformly decidable sets iff they are not Turing closed. Then, the partially ordered set of Turing closed fields is proved isomorphic to...

1.5∗ (A.Ostaszewski, email 9-92) Consider Telgarsky’s game G(T ) where T ⊆ 2. Player I plays a countable cover of T Player II chooses onesay Xn. Player I wins iff ∩{cl(Xn) : n ∈ ω} ⊆ T . It is known that (a) Player I has winning strategy iff T is analytic. (b) If there exists A an analytic subset of cl(T ) not Borel separated from T , then Player II has a winning strategy. Is the converse of (b...

We define an invariant β(M) of a finite volume hyperbolic 3manifoldM in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M . We show β(M) lies in a subgroup of B(C) of finite Q-rank determined by the invariant trace field of M . Moreover, the Chern-Simons invariant of M is determined modulo rationals by β(M). This leads to a simpl...

Let (S*, k(S2)) be a knot formed by spinning a polyhedral arc a. about the standard 2-sphere S" in the 3-sphere S3. Then the second homotopy group of S"—k(S2) as a Z^-module is isomorphic to each of the following: (1) The fundamental ideal modulo the left ideal generated by a—\, where a is the image in ■¡r1(Si—k(S2)) of a generator of (2) The first homology group of the kernel of ^(SP-hiS1))-* ...

In this paper, we will show a reduction of ideal arithmetic, or more generally, of arithmetic of ZZ{modules of full rank in orders of number elds to problems of linear algebra over ZZ=mZZ, where m is a possibly composite integer. The problems of linear algebra over ZZ=mZZ will be solved directly, instead of either \reducing" them to problems of linear algebra over ZZ or factoring m and working ...

We deene an invariant (M) of a nite volume hyperbolic 3-manifold M in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M. We show (M) lies in a subgroup of B(C) of nite Q-rank determined by the invariant trace eld of M. Moreover, the Chern-Simons invariant of M is determined modulo ra-tionals by (M). This leads to a simplicial for...