15,680 research outputs found
Non-commutative solitons and strong-weak duality
Some properties of the non-commutative versions of the sine-Gordon model
(NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our
method relies on the NC extension of integrable models and the master
Lagrangian approach to deal with dual theories. The master Lagrangians turn out
to be the NC versions of the so-called affine Toda model coupled to matter
fields (NCATM) associated to the group GL(2), in which the Toda field belongs
to certain representations of either or corresponding
to the Lechtenfeld et al. (NCSG) or Grisaru-Penati (NCSG) proposals
for the NC versions of the sine-Gordon model, respectively. Besides, the
relevant NCMT models are written for two (four) types of Dirac fields
corresponding to the Moyal product extension of one (two) copy(ies) of the
ordinary massive Thirring model. The NCATM models share the same
one-soliton (real Toda field sector of model 2) exact solutions, which are
found without expansion in the NC parameter for the corresponding Toda
and matter fields describing the strong-weak phases, respectively. The
correspondence NCSG NCMT is promising since it is
expected to hold on the quantum level.Comment: 24 pages, 1 fig., LaTex. Typos in star products of eqs. (3.11)-(3.13)
and footnote 1 were corrected. Version to appear in JHE
Semiparametric Cross Entropy for rare-event simulation
The Cross Entropy method is a well-known adaptive importance sampling method
for rare-event probability estimation, which requires estimating an optimal
importance sampling density within a parametric class. In this article we
estimate an optimal importance sampling density within a wider semiparametric
class of distributions. We show that this semiparametric version of the Cross
Entropy method frequently yields efficient estimators. We illustrate the
excellent practical performance of the method with numerical experiments and
show that for the problems we consider it typically outperforms alternative
schemes by orders of magnitude
Estimator Selection: End-Performance Metric Aspects
Recently, a framework for application-oriented optimal experiment design has
been introduced. In this context, the distance of the estimated system from the
true one is measured in terms of a particular end-performance metric. This
treatment leads to superior unknown system estimates to classical experiment
designs based on usual pointwise functional distances of the estimated system
from the true one. The separation of the system estimator from the experiment
design is done within this new framework by choosing and fixing the estimation
method to either a maximum likelihood (ML) approach or a Bayesian estimator
such as the minimum mean square error (MMSE). Since the MMSE estimator delivers
a system estimate with lower mean square error (MSE) than the ML estimator for
finite-length experiments, it is usually considered the best choice in practice
in signal processing and control applications. Within the application-oriented
framework a related meaningful question is: Are there end-performance metrics
for which the ML estimator outperforms the MMSE when the experiment is
finite-length? In this paper, we affirmatively answer this question based on a
simple linear Gaussian regression example.Comment: arXiv admin note: substantial text overlap with arXiv:1303.428
Thermal Entanglement of a Spin-1/2 Ising-Heisenberg Model on a Symmetrical Diamond Chain
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a
symmetrical diamond chain were analyzed. Due to the separable nature of the
Ising-type exchange interactions between neighboring Heisenberg dimers,
calculation of the entanglement can be performed exactly for each individual
dimer. Pairwise thermal entanglement was studied in terms of the isotropic
Ising-Heisenberg model, and analytical expressions for the concurrence (as a
measure of bipartite entanglement) were obtained. The effects of external
magnetic field and next-nearest neighbor interaction between nodal
Ising sites were considered. The ground-state structure and entanglement
properties of the system were studied in a wide range of the coupling constant
values. Various regimes with different values of the ground-state entanglement
were revealed, depending on the relation between competing interaction
strengths. Finally, some novel effects, such as the two-peak behavior of
concurrence versus temperature and coexistence of phases with different values
of magnetic entanglement were observed
Optimal Joins Using Compact Data Structures
Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice. However, the implementation of these algorithms often requires an enhanced indexing structure: to achieve optimality we either need to build completely new indexes, or we must populate the database with several instantiations of indexes such as B+-trees. Either way, this means spending an extra amount of storage space that may be non-negligible.
We show that optimal algorithms can be obtained directly from a representation that regards the relations as point sets in variable-dimensional grids, without the need of extra storage. Our representation is a compact quadtree for the static indexes, and a dynamic quadtree sharing subtrees (which we dub a qdag) for intermediate results. We develop a compositional algorithm to process full join queries under this representation, and show that the running time of this algorithm is worst-case optimal in data complexity. Remarkably, we can extend our framework to evaluate more expressive queries from relational algebra by introducing a lazy version of qdags (lqdags). Once again, we can show that the running time of our algorithms is worst-case optimal
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