11,133 research outputs found
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 has a parasupersymmetry of order
and a fractional supersymmetry of order .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
- …