39,396 research outputs found
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
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 and , which determine
respectively the slope of the scalar field potential and the dark matter-dark
energy coupling strength, can be constrained to and 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 tightens the bound on by a factor of
two, although this apparent improvement is arguably an artefact of the tension
between the local measurement and the value inferred from Planck data in
the minimal 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
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
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
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