It was proved few years ago that classes of Boolean functions definable by means of functional equations [9], or equivalently, by means of relational constraints [15], coincide with initial segments of the quasi-ordered set (Ω,≤) made of the set Ω of Boolean functions, suitably quasi-ordered. The resulting ordered set (Ω/ ≡,⊑) embeds into ([ω] ,⊆), the set -ordered by inclusionof finite subsets...

Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework for contracting edges of a graph (merging vertices into super-vertices) with the goal of preserving pairwise distances as accurately as possible. Formally, given an edge-weighted graph, the contraction s...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

In this paper, we consider an intensity modulated direct detection multiple-input-multiple-output optical wireless communication (IM/DD MIMO-OWC) system, where the channel coefficients are assumed to be completely known at the receiver. For such a system, since both the transmitted signals and the channel coefficients are nonnegative, the full rank condition on the unique identification of the ...

A new pair of asymptotic invariants for finitely presented groups, called intrinsic and extrinsic tame filling functions, are introduced. These filling functions are quasi-isometry invariants that strengthen the notions of intrinsic and extrinsic diameter functions for finitely presented groups. We show that the existence of a (finite-valued) tame filling function implies that the group is tame...

An extension of the infomax algorithm of Bell and Sejnowski (1995) is presented that is able to blindly separate mixed signals with suband super-Gaussian source distributions. This was achieved by using a simple type of learning rule rst derived by Girolami (1997) by choosing negentropy as a projection pursuit index. Parameterized probability distributions that have suband super-Gaussian regime...

We consider pairs of finitely presented, residually finite groups P ↪→ Γ for which the induced map of profinite completions P̂ → Γ̂ is an isomorphism. We prove that there is no algorithm that, given an arbitrary such pair, can determine whether or not P is isomorphic to Γ. We construct pairs for which the conjugacy problem in Γ can be solved in quadratic time but the conjugacy problem in P is uns...

Bounded Reverse Mathematics Phuong Nguyen Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2008 First we provide a unified framework for developing theories of Bounded Arithmetic that are associated with uniform classes inside polytime (P) in the same way that Buss’s theory S2 is associated with P. We obtain finitely axiomatized theories many of which turn out ...

The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion ofthe theory ofinner measures, their construction, and the relationship oftheir prop...