On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.Comment: 13 pages, to appear in J. Phys. A: Math. Ge

Localizing the Latent Structure Canonical Uncertainty: Entropy Profiles for Hidden Markov Models

This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state uncertainty. The entropy of the state sequence that explains an observed sequence for a given hidden Markov chain model can be considered as the canonical measure of state sequence uncertainty. This canonical measure of state sequence uncertainty is not reflected by the classic multivariate state profiles computed by the smoothing algorithm, which summarizes the possible state sequences. Here, we introduce a new type of profiles which have the following properties: (i) these profiles of conditional entropies are a decomposition of the canonical measure of state sequence uncertainty along the sequence and makes it possible to localize this uncertainty, (ii) these profiles are univariate and thus remain easily interpretable on tree structures. We show how to extend the smoothing algorithms for hidden Markov chain and tree models to compute these entropy profiles efficiently.Comment: Submitted to Journal of Machine Learning Research; No RR-7896 (2012

The effect of vacuum polarisation on muon-proton scattering at small energies and angles

We give a compact expression for the unpolarised differential cross section for muon-proton scattering in the one photon exchange approximation. The effect of adding the vacuum polarisation amplitude to the no-spin-flip amplitude for one photon exchange is calculated at small energies and scattering angles and is found to be negligible for present experiments.Comment: 6 pages, one figur

Mechanically Compliant Grating Reflectors for Optomechanics

We demonstrate micromechanical reflectors with a reflectivity as large as 99.4% and a mechanical quality factor Q as large as 7.8*10^5 for optomechanical applications. The reflectors are silicon nitride membranes patterned with sub-wavelength grating structures, obviating the need for the many dielectric layers used in conventional mirrors. We have employed the reflectors in the construction of a Fabry-Perot cavity with a finesse as high as F=1200, and used the optical response to probe the mechanical properties of the membrane. By driving the cavity with light detuned to the high-frequency side of a cavity resonance, we create an optical antidamping force that causes the reflector to self-oscillate at 211 kHz

Fixed Point and Aperiodic Tilings

An aperiodic tile set was first constructed by R.Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals) We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. The flexibility of this construction allows us to construct a "robust" aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. This property was not known for any of the existing aperiodic tile sets.Comment: v5: technical revision (positions of figures are shifted