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

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

How CMB and large-scale structure constrain chameleon interacting dark energy

We explore a chameleon type of interacting dark matter-dark energy scenario in which a scalar field adiabatically traces the minimum of an effective potential sourced by the dark matter density. We discuss extensively the effect of this coupling on cosmological observables, especially the parameter degeneracies expected to arise between the model parameters and other cosmological parameters, and then test the model against observations of the cosmic microwave background (CMB) anisotropies and other cosmological probes. We find that the chameleon parameters $\alpha$ and $\beta$, which determine respectively the slope of the scalar field potential and the dark matter-dark energy coupling strength, can be constrained to $\alpha < 0.17$ and $\beta < 0.19$ using CMB data alone. The latter parameter in particular is constrained only by the late Integrated Sachs-Wolfe effect. Adding measurements of the local Hubble expansion rate $H_0$ tightens the bound on $\alpha$ by a factor of two, although this apparent improvement is arguably an artefact of the tension between the local measurement and the $H_0$ value inferred from Planck data in the minimal $\Lambda$CDM model. The same argument also precludes chameleon models from mimicking a dark radiation component, despite a passing similarity between the two scenarios in that they both delay the epoch of matter-radiation equality. Based on the derived parameter constraints, we discuss possible signatures of the model for ongoing and future large-scale structure surveys.Comment: 25 pages, 6 figure

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

On the second moment for primes in an arithmetic progression

Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a constant factor of the conjectured asymptotic result for the second moment for primes in an individual arithmetic progression in short intervals. Previous results were averaged over all progression of a given modulus. The method uses a short divisor sum approximation for the von Mangoldt function, together with some new results for binary correlations of this divisor sum approximation in arithmetic progressions