Acyclic Jacobi Diagrams

We propose a simple new combinatorial model to study spaces of acyclic Jacobi diagrams, in which they are identified with algebras of words modulo operations. This provides a starting point for a word-problem type combinatorial investigation of such spaces, and provides fresh insights on known results.Comment: 18 pages, 7 figures. Refernces added. Section 2 rewritten. Proof of Theorem 1.1 rewritten. To appear in Kobe J. Mat

Vanishing of 3-Loop Jacobi Diagrams of Odd Degree

We prove the vanishing of the space of 3-loop Jacobi diagrams of odd degree. This implies that no 3-loop finite-type invariant can distinguish between a knot and its inverse.Comment: 13 pages. Section on the even degree case expanded. Various minor correction

Tsirelson's Bound Prohibits Communication Through a Disconnected Channel

Why does nature only allow nonlocal correlations up to Tsirelson's bound and not beyond? We construct a channel whose input is statistically independent of its output, but through which communication is nevertheless possible if and only if Tsirelson's bound is violated. This provides a statistical justification for Tsirelson's bound on nonlocal correlations in a bipartite setting.Comment: 9 pages, 2 figures. Title and abstract modified, exposition simplifie

Low-Dimensional Topology of Information Fusion

We provide an axiomatic characterization of information fusion, on the basis of which we define an information fusion network. Our construction is reminiscent of tangle diagrams in low dimensional topology. Information fusion networks come equipped with a natural notion of equivalence. Equivalent networks `contain the same information', but differ locally. When fusing streams of information, an information fusion network may adaptively optimize itself inside its equivalence class. This provides a fault tolerance mechanism for such networks.Comment: 8 pages. Conference proceedings version. Will be superceded by a journal versio

Computing with Coloured Tangles

We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of computation is Turing complete, and that with bounded resources it can moreover decide any language in complexity class IP, sometimes with better performance parameters than corresponding classical protocols.Comment: 36 pages,; Introduction entirely rewritten, Section 4.3 adde