57,919 research outputs found
Cluster ensembles, quantization and the dilogarithm
Cluster ensemble is a pair of positive spaces (X, A) related by a map p: A ->
X. It generalizes cluster algebras of Fomin and Zelevinsky, which are related
to the A-space. We develope general properties of cluster ensembles, including
its group of symmetries - the cluster modular group, and a relation with the
motivic dilogarithm. We define a q-deformation of the X-space. Formulate
general duality conjectures regarding canonical bases in the cluster ensemble
context. We support them by constructing the canonical pairing in the finite
type case.
Interesting examples of cluster ensembles are provided the higher Teichmuller
theory, that is by the pair of moduli spaces corresponding to a split reductive
group G and a surface S defined in math.AG/0311149.
We suggest that cluster ensembles provide a natural framework for higher
quantum Teichmuller theory.Comment: Version 7: Final version. To appear in Ann. Sci. Ecole Normale. Sup.
New material in Section 5. 58 pages, 11 picture
Weight Distribution for Non-binary Cluster LDPC Code Ensemble
In this paper, we derive the average weight distributions for the irregular
non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we
give the exponential growth rate of the average weight distribution in the
limit of large code length. We show that there exist -regular
non-binary cluster LDPC code ensembles whose normalized typical minimum
distances are strictly positive.Comment: 12pages, 6 figures, To be presented in ISIT2013, Submitted to IEICE
Trans. Fundamental
A CLUE for CLUster Ensembles
Cluster ensembles are collections of individual solutions to a given clustering problem which are useful or necessary to consider in a wide range of applications. The R package clue provides an extensible computational environment for creating and analyzing cluster ensembles, with basic data structures for representing partitions and hierarchies, and facilities for computing on these, including methods for measuring proximity and obtaining consensus and "secondary" clusterings.
Generation of pure continuous-variable entangled cluster states of four separate atomic ensembles in a ring cavity
A practical scheme is proposed for creation of continuous variable entangled
cluster states of four distinct atomic ensembles located inside a high-finesse
ring cavity. The scheme does not require a set of external input squeezed
fields, a network of beam splitters and measurements. It is based on nothing
else than the dispersive interaction between the atomic ensembles and the
cavity mode and a sequential application of laser pulses of a suitably adjusted
amplitudes and phases. We show that the sequential laser pulses drive the
atomic "field modes" into pure squeezed vacuum states. The state is then
examined against the requirement to belong to the class of cluster states. We
illustrate the method on three examples of the entangled cluster states, the
so-called continuous variable linear, square and T-type cluster states.Comment: 9 pages, 3 figure
Storage and retrieval of continuous-variable polarization-entangled cluster states in atomic ensembles
We present a proposal for storing and retrieving a continuous-variable
quadripartite polarization-entangled cluster state, using macroscopic atomic
ensembles in a magnetic field. The Larmor precession of the atomic spins leads
to a symmetry between the atomic canonical operators. In this scheme, each of
the four spatially separated pulses passes twice through the respective
ensemble in order to map the polarization-entangled cluster state onto the
long-lived atomic ensembles. The stored state can then be retrieved by another
four read-out pulses, each crossing the respective ensemble twice. By
calculating the variances, we analyzed the fidelities of the storage and
retrieval, and our scheme is feasible under realistic experimental conditions.Comment: 6 pages, 4 figure
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